Vol. 84, No. 1, 1979

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2-factorization in finite groups

Makoto Hayashi

Vol. 84 (1979), No. 1, 97–142
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 NG(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)CH(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
Authors
Makoto Hayashi