JOURNAL OF ALGEBRA 111, 365-383 (1987) A Classification of the Maximal Subgroups of the Finite Alternating and Symmetric Groups MARTIN W. LIEBECK Imperial College, London, S W7, England CHERYL E. F'RAEGER University of Western Australia, Nedlands, Western Australia 6009 AND JAN SAXL Gonville and Caius College, Cambridge, England Received January 13, 1986 1. INTRODUCTION AND STATEMENT OF RESULTS 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 degreesn: n =pa with p prime [7]; n=kpwithpprime,k<p [21]; n any odd number [ 14,221. Nevertheless, the general problem of listing all the maximal subgroups of 365 0021~8693/87 $3.00 Copyright 0 1987 by Academic Press, Inc. Ali rights of reproduction in any form reserved. brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by Elsevier - Publisher Connector