# Jerusalem Mathematics Colloquium

Thursday, 26 March 1998, 4:00 pm

Mathematics Bldg., lecture hall 2

## Prof. Yoav Segev (Ben Gurion Uni. of the Negev)

Are finite quotients of the multiplicative group of a division
algebra solvable?

** Abstract: **

Recall that a division algebra (sometimes called a skewfield) is a
field except that multiplication is NOT commutative. A division
algebra has finite dimension if its dimension (as a vector space)
over its center (which is a field) is finite.

Recall that solvable groups are constructed by the "rule" that abelian
groups are solvable and if G is a group with a normal subgroup N such that
N and G/N are solvable, then G is solvable.

The structure of the multiplicative group of division algebras is
pretty mysterious, even though they've been around for quite sometime. It
is known however that they are never solvable. Recent results suggest
that the following conjecture is true

CONJECTURE F.SO.Q (finite solvable quotients): Finite quotients
of the multiplicative group of a finite dimensional division
algebra are solvable.

We'll discuss Conjecture F.So.Q. and connect it to a long standing
open conjecture of Margulis and Platonov on the normal subgroup structure
of algebraic groups over number fields.

Coffee, Cookies at the faculty lounge at 3:30.

Come to the "after colloquium coffee chat" in Beit-Belgia.

List of talks, fall 1997