On Thompson's simple group

Abstract

Recently, Thompson [9] constructed a new simple group E of order 2 15 ∘ 3 105 37 2 ∘ 13 ∘ 19 ∘ 31 = 90, 745, 943, 887, 872, 000. In particular, E contains only one conjugacy class of involutions, and if e is an involution in E then C E ( e) is a (nonsplit) extension of an extra-special 2-group of order 2 9 by A 9, the alternating group of degree 9. The aim of this paper is to prove the following result.