On the maximum orders of elements of finite almost simple groups and\n primitive permutation groups

2013/01/22 by Simon D. Guest, Joy Morris, Guest, Simon +5 · 7 citations
Mathematics · Computer Science · Engineering · #Finite Group Theory Research #Coding theory and cryptography #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1301.5166

Abstract

We determine upper bounds for the maximum order of an element of a finite\nalmost simple group with socle T in terms of the minimum index m(T) of a\nmaximal subgroup of T: for T not an alternating group we prove that, with\nfinitely many exceptions, the maximum element order is at most m(T). Moreover,\napart from an explicit list of groups, the bound can be reduced to m(T)/4.\nThese results are applied to determine all primitive permutation groups on a\nset of size n that contain permutations of order greater than or equal to n/4.\n

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