London Algebra Colloquium abstract
Counting prime order subgroups of finite groups
Tim Burness (Southampton), 23rd October 2008
Abstract
Let G be a finite group, let i2(G) be the number of involutions
in G and let δ(G) be the number of
prime order subgroups of G. In 1970, C.T.C. Wall classified the finite groups
G with i2(G) > |G|/2 − 1. In
recent work with Stuart Scott, we extend Wall’s theorem by determining the groups
G with δ(G) > |G|/2 − 1.
The proof uses the Classification of Finite Simple Groups,
and some interesting results are obtained along the way.
I will describe our motivations for studying this problem and I
will explain the main steps in the proof. I
will also outline an application of the main theorem to the prime
generation problem in finite near-rings, and
discuss some related results and open problems.