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

Guest, S., Morris, J., Praeger, C., Spiga, P. (2015). On the maximum orders of elements of finite almost simple groups and primitive permutation groups. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 367(11), 7665-7694 [10.1090/S0002-9947-2015-06293-X].

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

SPIGA, PABLO
Ultimo
2015

Abstract

We determine upper bounds for the maximum order of an element of a finite almost simple group with socle T in terms of the minimum index m(T) of a maximal subgroup of T: for T not an alternating group we prove that, with finitely many exceptions, the maximum element order is at most m(T). Moreover, apart from an explicit list of groups, the bound can be reduced to m(T)/4. These results are applied to determine all primitive permutation groups on a set of size n that contain permutations of order greater than or equal to n/4.
Articolo in rivista - Articolo scientifico
group theory
English
7665
7694
30
Guest, S., Morris, J., Praeger, C., Spiga, P. (2015). On the maximum orders of elements of finite almost simple groups and primitive permutation groups. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 367(11), 7665-7694 [10.1090/S0002-9947-2015-06293-X].
Guest, S; Morris, J; Praeger, C; Spiga, P
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/99629
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