The length of a finite group G is defined to be the maximal length of an unrefinable chain of subgroups going from G to 1. This notion was studied by many authors since the 1940s.

Recently there is growing interest also in the depth of G, which is the minimal length of such a chain. Moreover, similar notions were defined and studied for important families of infinite groups, such as connected algebraic groups and connected Lie groups.

I will describe recent works on these topics, joint with Tim Burness and Martin Liebeck. The proofs use a variety of tools, including recent results in analytic number theory.

Recently there is growing interest also in the depth of G, which is the minimal length of such a chain. Moreover, similar notions were defined and studied for important families of infinite groups, such as connected algebraic groups and connected Lie groups.

I will describe recent works on these topics, joint with Tim Burness and Martin Liebeck. The proofs use a variety of tools, including recent results in analytic number theory.

## Date:

Tue, 26/06/2018 - 15:00 to 16:00

## Location:

Manchester House, Lecture Hall 2