137

Random Steiner systems and bounded degree coboundary expanders of every dimension

Alexander Lubotzky, Zur Luria and Ron Rosenthal

 

 

 

pdf 

136

A trichotomy theorem for tranaformation groups of locally symmetric manifolds and topological rigidity

Sylvain Cappell, Alexander Lubotzky, and Shmuel Weinberger

 

 

 

pdf 

135

Presentations: from Kac-Moody groups to profinite and back

I. Capdebosoq, A. Lubotzky and B. Remy

 

to appear

 

 

 

134

Sliceable groups and towers of fields

S. Boge, M. Jarden and A. Lubotzky

 

Journal of Group Theory, to appear

 

 

pdf 

133

Mixing properties and the chromatic number of Ramanujan complexes

S. Evra, C. Golubev and A. Lubotzky

 

 

 

pdf 

132

Isoperimetric inequalities for Ramanujan complexes and topological expanders

T. Kaufman, D. Kazhdan and A. Lubotzky

 

preprint

 

 

pdf 

131

Invariable generation of infinite groups

W.M. Kantor, A. Lubotzky and A. Shalev

 

Journal of Algebra, to appear

 

 

pdf 

130

The Masorah as error correcting code

Y. Ofer and A. Lubotzky

 

Tarbitz Vol. LXXXII (2013) 89–114 (Hebrew)

 

 

pdf 

129

Random methods in 3-manifold theory

A. Lubotzky, J. Maher and C. Wu

 

 

 

pdf 

128

Expansion of Building-Like Complexes

A. Lubotzky, R. Meshulam and S. Mozes

 

 

 

pdf 

127

Isoparametric inequalities for Ramanujan complexes and topological overlapping

T. Kaufman, D. Kazhdan and A. Lubotzky

 

FOCS 2014, Proceedings of Foundation of Computer Science, to appear

 

 

 

126

Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds

L. Guth and A. Lubotzky

 

Journal of Mathematical Physics, 55,082202(2014)

 

 

pdf 

125

Random Latin squares and 2-dimensional expanders

A. Lubotzky and R. Meshulam

 

 

 

pdf 

124

High dimensional expanders and property testing

T. Kaufman and A. Lubotzky

 

ITCS 2014 Proceedings of the 5th conference on Innovatinos in theoretical computer science, pp. 501-506, ACM New York

 

 

pdf 

123

Arithmetic quotients of the mapping class group

F. Grunewald, M. Larsen, A. Lubotzky and J. Malestein

 

Geometric and Functional Analysis (GAFA), to appear

 

 

pdf 

122

Finiteness Properties and Profinite Completions

A. Lubotzky

 

Bull. London Math. Soc. 46 (2014), 103–110

 

 

pdf 

121

Images of word maps in finite simple groups

A. Lubotzky

 

Glasgow Math. J. 56 (2014), no. 2, 465–469

 

 

pdf 

120

Ramanujan complexes and High Dimensional Expanders

A. Lubotzky

 

Japanese Journal of Mathematics, to appear

 

 

pdf 

119

Deformation theory and finite simple quotients of triangle groups II

M. Larsen, A. Lubotzky and C. Marion

 

Groups, Geometry and Dynamics (GGD), to appear

 

 

pdf 

118

Deformation theory and finite simple quotients of triangle groups I

M. Larsen, A. Lubotzky and C. Marion

 

European J. Math. (JEMS) 16 (2014), 1349–1375

 

 

pdf 

117

The Galois group of random elements of linear groups

A. Lubotzky and L. Rosenzweig

 

American J. of Math., to appear

 

 

pdf 

116

Representation varieties of Fuchsian groups

M. Larsen, A. Lubotzky

2013

From Fourier analysis and number theory to radon transforms and geometry, 375–397, Dev. Math., 28, Springer, New York, 2013

 

 

pdf 

115

Edge transitive Ramanujan graphs and symmetric LDPC good codes

T. Kaufman and A. Lubotzky

2012

STOC’12—Proceedings of the 2012 ACM Symposium on Theory of Computing, 359–365, ACM, New York, 2012

 

 

pdf 

114

Manifolds counting and class field towers

M. Beliolipetsky, A. Lubotzky

2012

Advances in Mathematics 229 (2012) 3123-3146

 

 

pdf 

113

Sieve methods in group theory III: Aut(Fn)

A. Lubotzky and C. Meiri

2012

Internat. J. of Algebra Comput. 22 (2012) 1250062, 8pp

 

 

pdf 

112

Sieve methods in group theory II: the mapping class group

A. Lubotzky and C. Meiri

2012

Geom. Dedicata 159 (2012), 327–336

 

 

pdf 

111

Expander graphs in pure and applied mathematics

A. Lubotzky

2012

Bull. AMS (N.S.) 49 (2012), 113–162

 

 

pdf 

110

Sieve method in group theory I. Powers in linear groups

A. Lubotzky and C. Meiri

2012

J. Amer. Math. Soc. 25 (2012), 1119–1148

 

 

pdf 

109

Conjugacy growth of linear groups

E. Breuillard, Y. de Cornulier, A. Lubotzky and C. Meiri

2013

Math. Proc. Comb. Phil. Soc. (2013), 261–277

 

 

pdf 

108

Beauville surfaces and finite simple groups

S. Garion, M. Larsen and A. Lubotzky

2012

J. Reine Angew. Math. (Crelle’s Journal) 666 (2012), 225–243

 

 

pdf 

107

Invariable generation and the Chebotarev invariant of a finite group

W. M. Kantor, A. Lubotzky and A. Shalev

2011

Journal of Algebra 348 (2011), 302-314

 

 

pdf 

106

Lattices with and lattices without spectral gap

B. Bekka and A. Lubotzky

2011

Groups, Geometry and Dynamics 5 (2011), 251-264

 

 

pdf 

105

Remarks on Proeficient groups

R. M. Guralnick,W. M. Kantor, M. Kassabov and A. Lubotzky

2011

Journal of Algebra, 326 (2011), 169-189

 

 

pdf 

104

Finite simple groups of Lie type as expanders

A. Lubotzky

2011

J. of the European Math. Soc., 13 (2011), 1331-1341

 

 

pdf 

103

The dynamic of Aut(Fn)-actions on group presentations and representation

A. Lubotzky

2011

in a special volume dedicated to R.J. Zimmer

 

 

pdf 

102

Presentation of finite simple groups: a computational approach

R.M. Guralnick, W.M. Kantor, M. Kassabov, A. Lubotzky

2011

J. of the European Math. Soc. (JEMS), 13 (2011), 391-458 

dvi

ps

pdf

101

Linear representations of the automorphism groups of free groups

F. Grunewald , A. Lubotzky

2009

Geometric and Functional Analysis (GAFA),18 (2009), 1564-1608

dvi

ps

pdf

100

Counting arithmetic lattices and surfaces, Annals of Mathematics

M. Belolipetsky, T. Gelander, A. Lubotzky and A. Shalev

2010

Annals of Mathematics 172 (2010), 2197-2221

 

 

pdf 

99

Representation growth for linear groups

M. Larsen, A. Lubotzky

2008

J. of the European Math. Soc. 10 (2008), 351–390 

dvi

ps

pdf

98

Heegard genus and property tau for hyperbolic 3-manifolds

D. D. Long, A. W. Reid, A. Lubotzky

2008

J. Topol. 1 (2008), no. 1, 152-158

dvi

ps

pdf

97

Elementary equivalence of profinite groups

M. Jarden, A. Lubotzky

2008

Bull. London Math. Soc. 40 (2008), 887–896 

 

 

pdf

96

Dimension expanders

E. Zelmanov, A. Lubotzky

2006

J. Algebra 319 (2008), no. 2,

730-738

dvi

ps

pdf

95

Presentation of Finite Simple Groups: A Quantitative Approach

R.M. Guralnick, W.M. Kantor, M. Kassabov, A. Lubotzky

2008

Journal of the American Math. Soc. 21 (2008), 711–774 

dvi

ps

pdf

94

Presentation of finite simple groups: cohomological and profinite approaches

R.M. Guralnick, W.M. Kantor, M. Kassabov, A. Lubotzky

2006

Groups Geom. Dyn. 1 (2007),

no. 4, 469-523.

 dvi

ps

pdf

93

A Moore bound for simplicial complexes

A. Lubotzky, R. Meshulam

2006

Bull. Lond. Math. Soc. 39 (2007), no. 3, 353-358

 

 

pdf

92

Finite simple groups as expanders

M. Kassabov, A. Lubotzky, N. Nikolov

2006

PNAS. 103, 6116-6119

dvi

ps

pdf

91

On Presentations and Second Cohomology of Some Finite Groups

I. Korchagina, A. Lubotzky

2006

Publ. Math. Debrecen 69 (2006), no. 3, 341-352

dvi

 

pdf

90

Isospectral Cayley graphs of some finite simple groups

A. Lubotzky, B. Samuels, U. Vishne

2006

Duke Math j.135 (2006), no.2, 381-393

dvi

ps

pdf

89

Division algebras and noncommensurable isospectral manifolds

A. Lubotzky, B. Samuels, U. Vishne

2006

Duke Math j.135 (2006), no.2, 361-379

dvi

ps

pdf

88

Finite prepresentation of adelic groups, the congruence kernel and cohomology of finite simple groups

A. Lubotzky

2005

Quarterly of Pure and Applied Mathematics (Borel Volume), 1, 241-256

dvi

 ps

pdf

87

Finite groups and hyperbolic manifolds

M. Belolipetsky, A. Lubotzky

2005

Invent. Math.162, 459-472

 dvi

 ps

 pdf

86

Some more super-rigid groups, in:"Geometry, Graphs and Dynamics: Proceedings in Memory of Robert Brooks"

A. Lubotzky

2005

Israel Mathematical Conference Proceeding, Contemporary Mathematics, AMS 387, 273-244

 

ps

pdf

85

Counting primes, groups and manifolds

D. Goldfeld, A. Lubotzky, N. Nikolov, L. Pyber

2004

Proc. of National Acad. of Sci. USA, 101, 13428-13430

dvi

 

pdf

84

Subgroup growth of lattices in semi-simple groups

A. Lubotzky, N. Nikolov

2004

Acta. Math. 193, 105-139

 

ps

pdf

83

Explicit construction of Ramanujan complexes of type Ad

A. Lubotzky, B. Samuels, V Vishne

2005

Europ. J. of Combinatorics. 26, 965-993

dvi

ps

pdf

82

Ramanujan complexes of type Ad

A. Lubotzky, B. Samuels, V. Vishne

2005

Israel J. Math. 149, 267-299

dvi

ps

pdf

81

The Finitary Andrew-Curtis Conjecture, in: Infinite Groups: geometric, combinatorial and dinamical aspects

A. Borovik, A. Lubotzky, A. Myasmikov

2005

Progress in Math. 248,

15-30

dvi

ps

pdf

80

Polynomial representation growth and the congruence subgroup problem

A. Lubotzky, B. Martin

2004

Israel J. of Math. 144, 293-316

dvi

ps

pdf

79

Finite representations in the unitary dual and ramanujan groups

A. Lubotzky, Y. Shalom

2004

AMS Contemporary Math. 347, 173-189

 

ps

pdf

78

Counting congruence subgroups

D. Goldfeld, A. Lubotzky, L. Pyber

2004

Acta Math. 193, 73-104

 

ps

pdf

77

The expected number of random elements to generate a finite group

A. Lubotzky

2002

J. of Algebra 257 452-459

dvi

ps

pdf

76

Bounded generation and linear groups

M. Abert, A Lubotzky

2003

Internat. J. Algebra Comput. 13, no. 4, 401-413

dvi

ps

pdf

75

Counting hyperbolic manifolds

M. Burger, T Gelander, A Lubotzky, S Mozes

2002

Geometric and Functional Analysis 12 1161-1173

 

 

pdf

74

On linear groups of polynomal normal subgroup growth; the (G2 F4 E8) theorem

M. Larsen, A. Lubotzky

2001

Algebraic groups & Arithmetic, Ed. S.G.Dani, G. Prasad, Tata inst. Fund. Res. Stud. Math. 441-468, TIFR, Mumbai

dvi

ps

pdf

73

Semi-direct product in groups and zig-zag product in graphs

N. Alon, A. Lubotzky, A Wigderson

2001

Proc. 42 IEEE FOCS 630-637

 

 

pdf

72

The pro-algebraic completion of rigid groups

H. Bass, A Lubotzky, A Magid, S. Moses

2002

Geom. Dedicata 95 19-58

 

ps

pdf

71

Profinite presentations

A Lubotzky

2001

J. of Algebra 242 672-690

 

 

 

70

Product replacement algorithm and Kazhdan property

A Lubotzky, I. Pak

2001

J. American Math. Soc. 14 347-363

 

 

 

69

Enumerating boundedly generated finite groups

A. Lubotzky

2001

J. of Algebra 238 194-199

 

 

 

68

Rank one phenomena for mapping class groups

A. Lubotzky, Y. Minsky, B. Farb

2001

Duke J. of Math. 106 581-597

 

 

 

67

A charachterization of S-arithmetic groups in higher rank semi-simple groups

A. Lubotzky, T.N. Venkataramana

2002

Geom. Dedicata 90 1-28

 

 

 

66

Arithmetic Structure of fundemental groups and actions of semisimple Lie groups

A. Lubotzky, R.J. Zimmer

2001

Topology 40 851-869

 

 

 

65

The word and Riemannian metrics on lattices of semi-simple groups

A Lubotzky, S. Mozes, M.S. Raghunathan

2000

Publ. Math. IHES 91 5-53

 

 

 

64

Non Arithmetic, Super rigid groups: Conterexamples to Platonov's conjecture

H. Bass, A Lubotzky

2000

Ann. of Math 151 1151-1173

 

 

 

63

Random normal subgroups of free pro finite groups

M. Jarden, A Lubotzky

1999

J. of Group Theory 2 213-224

 

 

 

62

Lattices of minimal covolume in SL2 over non archimeadean fields

A. Lubotzky, T Weigel

1999

Proc. London Math Soc. 78 283-333

 

 

 

61

One for allmost all: Generation of SL(n,p) by subsets of SL(n,Z)

A Lubotzky

1999

Contemporary Math. 243 125-128 AMS Providence RI

 

 

 

60

Not every uniform tree covers Ramanujan graphs

A. Lubotzky, T. Nagnibeda

1998

J. Comb. Th. B 74 202-212

 

 

 

59

Eigenvalues of the Laplacian, The first Betti number and the congruence subgroup problem

A. Lubotzky

1997

Ann. of Math. 145 441-452

 

 

 

58

A Cannonical arithmetic quotient for simple Lie group actions

A. Lubotzky, R.J. Zimmer

1996

proc. of the conf. "Ergodic Theory and Lie Groups" Bombay

 

 

 

57

Free quotients and the first Betti number of some hyperbolic manifolds

A. Lubotzky

1996

Transformation Groups 171-82

dvi

ps

pdf

56

Discrete groups of subgroup growth

A. Lubotzky, L. Pyber, A. Shalev

1996

Israel J. of Math. 96 399-418

 

 

 

55

Functional equations and uniformity for local zeta functions of nilpotent groups

M.P.F Du Sautoy, A. Lubotzky

1996

Amer. J. of Math. 118 39-90

 

 

 

54

Powers in finitely generated groups

E. Hrushovsky, P.H. Kropholer, A. Lubotzky, A. Shalev

1996

Trans of the AMS 348 291-304

 

 

 

53

Counting finite index subgroups

A. Lubotzky

1995

lecture notes LMS 212 368-404 Cambridge Univ.

 

ps

pdf

52

Tree lattices and lattices in Lie groups

A. Lubotzky

1995

lecture notes LMS 204 217-232 Cambridge Univ.

 

 

 

51

Cayley graphs: eigenvalues, expanders and random walks

A. Lubotzky

1995

lecture notes LMS 218 155-189 Cambridge Univ.

 

 

 

50

Subgroup growth

A Lubotzky

1995

Proc. of Int. Congress of Math. 1 309-317 Birkhauzer

 

 

 

49

Subgroup growth and congruence subgroups

A. Lubotzky

1995

Invent. Math. 119 267-295

 

 

 

48

Linear central filtrations on groups

H. Bass, A. Lubotzky

1994

Contemporary Math. 169 AMS

 

 

 

47

Super rigidity for the commensurabilitygroup of tree lattices

A. Lubotzky, S. Moses, R.J. Zimmer

1994

Comment. Math. Helv. 69 523-548

 

 

 

46

Rigidity of groups actions on locally finite trees

H. Bass, A. Lubotzky

1994

Proc. Lond. Math. Soc. 69 541-575

 

 

 

45

On some analytic pro-p groups

A. Lubotzky, A. Shalev

1994

Israel J. of Math. 85 307-337

 

 

 

44

Cyclic subgroups of exponential growth and metrics on descerete groups

A. Lubotzky, S. Mozes, M.S. Raghunathan

1993

Adad. Sci. 317 735-740

 

 

pdf

43

Groups of expandness - in: "Expanding Graphs"

A. Lubotzky, B. Weiss

1993

DIMACS, series in descrete math. and theory of cs.

 

ps

pdf

42

Finitely generated groupsof polynomial subgroup growth

A. Lubotzky, A. Mann, D. Segal

1993

Israel J. of Math. 82 363-371

 

 

 

41

Torsion in profinite completion of torsion free groups

A. Lubotzky

1993

Oxford Quar. J. of Math. 44 327-332

 

 

pdf 

40

Random elements of free profinite group generate a free subgroup

A. Lubotzky

1993

Illinois J. of Math 37 78-84

 

 

 

39

Asymptotic properties of unitary representations of tree automorphysm

A. Lubotzky, S. Mozes

1992

Plenum Press, New York

 

 

 

38

Hilbertian fields and free profinite groups

A. Jarden, A. Lubotzky

1992

J. of the London Math. Soc.46 205-227

 

 

 

37

Lattices in rank one Lie groups over local fields

A. Lubotzky

1991

Geometric & Functional Anlysis 1 405-431

 

 

 

36

Groups of polynomyal subgroup growth

A. Lubotzky, A. Mann

1991

Inventiones Math. 104 521-533

 

 

 

35

On the diameter of finite groups

L. Babai, G. Hetyei, W.M. Kantor, A. Lubotzky, A. Seress

1990

proc. of "Foundations of CS 1990" (FOCS)

 

 

 

34

Lattices of minimal covolume in SL2 A non archemedean analogue of Siegel's theorem

A. Lubotzky

1990

J. of American Math. Soc. 3 961-975

 

 

 

33

The probability of generating a finite simple group

W.M. Kantor, A. Lubotzky

1990

Geom. Dedicata 36 67-87

 

 

 

32

Locally symmetric graphs of prescribed girth and coxeter groups

A. Lubotzky

1990

J. of Discrete Math. 3 177-180

 

 

 

31

Residually finite groups of finite rank

A. Lubotzky, A. Mann

1989

math. proc. of Cambridge Phil. Soc. 106 385-388

 

 

 

30

Variants of Kazhdan's property for discrete subgroups of semi-simple groups

A. Lubotzky, R.J. Zimmer

1989

Israel J. of Math. 66 289-299

 

 

 

29

Trees and discrete subgroups of Lie groups over local fields

A. Lubotzky

1989

Bull. Amer. Math. Soc. 20 27-30

 

 

 

28

Small diameter Cayley graphs for finite simple groups

L. Babai, W.M. Kantor, A Lubotzky

1989

Europ. J. of Combinatorics 10 507-522

 

 

 

27

Group theoretic characterization of linear groups

A. Lubotzky

1988

J. of Algebra 113207-214

 

 

 

26

Ramanujan graphs

A. Lubotzky, R. Phillips, P. Sarnak

1988

Combinatorica 8 261-277

 

 ps

pdf

25

Local structure of representation varieties

A. Lubotzky, A Magid

1987

proc. of "Geometry of Group Representation" Contemp. Math. 74 215-235 AMS

 

 

 

24

On finite index subgroups of linear groups.

A. Lubotzky

1987

Bull. London Math. Soc. 19 325-328

 

 

 

23

Hecke operators and distributing points on the sphere II

A. Lubotzky, R. Phillips, R. Sarnak

1987

Communications on Pure and Applied Math.40 401-420

 

 

 

22

Power-full p-groups II. p-adic analytic groups

A. Lubotzky, A. Mann

1987

J. of Algebra 105 506-515

 

 

 

21

Power-full p-groups I. Finite groups

A. Lubotzky, A. Mann

1987

J. of Algebra 105 485-505

 

 

 

20

Dimension function for discrete groups

A. Lubotzky

1986

Groups-St. Andrews 1985 254-262 Cambridge univ. press

 

 

 

19

Hecke operators and distributing points on the sphere I

A. Lubotzky, R. Phillips, R. Sarnak

1986

Communications on Pure and Applied Math. 39 149-186

 

 

 

18

Explicit expanders and the Ramanujan conjectures

A. Lubotzky, R. Phillips, R. Sarnak

1986

proc. of the 18th Annual ACM Symposium on Theory of Computing STOC 240-246

 

 

 

17

On problem of magnus,

A. Lubotzky

1986

proc. of the AMS 98 583-585

 

 

 

16

Maximal abelian subgroups of free profinite groups

D. Haran, A. Lubotzky

1985

proc. Cambridge Phil. Soc. 97 51-55

 

 

 

15

Cohomology, poincare series and group algebras of unipotent groups

A. Lubotzky, A. Magid

1985

Amer. J. of Math. 107 531-553

 

 

 

14

An embedding theorem for pro-finite groups

A. Lubotzky, J. Wilson

1984

Archiv der Mathematik 42 397-399

 

 

 

13

Abelian and solvable subgroups of the mapping class groups

J. Birman, A. Lubotzky, J. McCarthy

1983

Duke J. of Math. 50 1107-1120

 

 

 

12

Group presentations, p-adic analytic groups and lattices in SL (2,C)

A. Lubotzky

1983

Ann. of Math. 118 115-130

 

 

 

11

Automorphism of schemes and of subgroups of finite type

H. Bass, A. Lubotzky

1983

Israel J. of Math. 44 1-22

 

 

 

10

Free pro-unipotent groups

A. Lubotzky, A. Magid

1983

J. of Algebra 80 323-349

 

 

 

9

Unipotent and pro-unipotent groups; cohomology and presentations

A. Lubotzky, A. Magid

1982

Bulletin of AMS 7 251-254

 

 

 

8

Combinatorial group theory of pro-p groups

A. Lubotzky

1982

Journal of Pure and Applied Math. 25 311-325

 

 

 

7

Embedding covers and the theory of frobenius fields

D. Haran, A. Lubotzky

1982

Israel J. of Math. 41 181-202

 

 

 

6

Free quotients and the congruence kernel of SL (2)

A. Lubotzky

1982

J. of Algebra 77 411-418

 

 

 

5

Cohomology of unipotent and pro-unipotent groups

A. Lubotzky, A. Magid

1982

J.l of Algebra 74 76-95

 

 

 

4

Subgroups of free pro-finite groups and large subfields of Q

A. Lubotzky, L. Van den dreis

1981

Israel J. of Math. 39 25-45

 

 

 

3

Tannaka duality for discrete groups

A. Lubotzky

1980

Amer. J. of Math. 102 663-689

 

 

 

2

Normal automorphism of free groups

A. Lubotzky

1980

J. of Algebra

 

 

 

1

On a problem of Grothendiek

A. Lubotzky

1978

Proc. Algebraic Geometry meeting, Lecture notes in math. 732 374-383