Title: THE STRUCTURE OF THE FINITE NON-SIMPLE GROUPS WHICH POSSESS A SIMPLE GROUP AS THE MAXIMAL SUBGROUP
Abstract: In this paper, the structure of the finite non-simple groups which possess a simple group as the maximal subgroup is studied and solved.Let G be a finite group, H be a maximal subgroup of G, the main results are:1. If H is of order p (p: prime), G is the group of order p2, or the abelian group of order pq, or the minimal non-nilpotent group of order pqβ (p≠q2 primes, β: the exponent of q (mod p)); and2. If H is non-abelian and simple but G is not simple, G is one of the following groups:(i) H×K; H is a non-abelian simple group, K is of prime order. (ii) H1×H2; H1, H2 are isomorphic non-abelian simple groups. (iii) H≤G; G/H is of prime order, H is the non-abelian simple group which without normal complement in G. And(iv) G=HN; H∩N=1, H is a non-abelian simple group, N is a non-simple characteristic-simple group, and H irreducibly acts on N by conjugation.Further, the relations among the simple maximal subgroups of the finite group have also been discussed in this paper.
Publication Year: 1988
Publication Date: 1988-01-01
Language: en
Type: article
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