2-factorization in finite groups

Makoto Hayashi

Vol. 84 (1979), No. 1, 97–142

DOI: 10.2140/pjm.1979.84.97

Abstract

Let G be a finite group, and S be a nonidentity 2-subgroup of G. Then, it is naturally conjectured that there exists a nonidentity N_G(S)-invariant subgroup of S, whose normalizer contains all the subgroups H of G with the following properties: (α)S is a Sylow 2-subgroup of H; (β)H does not involve the symmetric group of degree four; and (γ)C_H(O₂(H)) ⊆ O₂(H). The purpose of this paper is to give a partial answer to this problem.

Mathematical Subject Classification 2000

Primary: 20D25

Milestones

Received: 10 April 1978

Revised: 14 December 1978

Published: 1 September 1979