A characteristic subgroup of a group of odd order

Zvi Arad and George Isaac Glauberman

Vol. 56 (1975), No. 2, 305–319

DOI: 10.2140/pjm.1975.56.305

Abstract

Let G be a finite solvable group of odd order. Suppose p is a prime, S is a Sylow p-subgroup of G, and O_ρ′(G) = 1. Let J(S) be the Thompson subgroup of S. Then, by a result of the second author (Lemma 6), Z(J(S)) ≈ G.

The object of this paper is to generalize the above result by replacing the prime p by a set of primes π.

Mathematical Subject Classification 2000

Primary: 20D10

Milestones

Received: 26 December 1973

Published: 1 February 1975