A classification of the maximal subgroups of the finite alternating and symmetric groups

Abstract

Following the classification of finite simple groups, one of the major problems in finite group theory today is the determination of the maximal subgroups of the almost simple groups-that is, of groups X such that X0 u X< Aut X, for some finite non-abelian simple group X0. The problem has been solved for most sporadic groups and groups of Lie type of low rank (see [ 19, Sects. 3, 43 for discussion and references). This paper is a contribution to the case where X0 is an alternating group A, (so that for n # 6, X is A, or S,). The maximal subgroups of A, and S, are known for several classes of degrees n: