π-homogeneity and π^′-closure of finite groups

Zvi Arad

Vol. 51 (1974), No. 1, 1–9

DOI: 10.2140/pjm.1974.51.1

Abstract

The purpose of this paper is to present a proof, under additional conditions, of the following conjecture: Let π be a set of primes, and let all π-subgroups of G be 2-closed. (If 2∉π, this condition is satisfied.) If G is π-homogeneous, then G is π′-closed.

Mathematical Subject Classification 2000

Primary: 20D20

Milestones

Received: 12 December 1972

Revised: 23 August 1973

Published: 1 March 1974