On overgroups of regular abelian p-groups

Edward Dobson

Abstract


Let G be a transitive group of odd prime-power degree whose Sylow p-subgroup P is abelian with t elementary divisors. We show that if p > 2t − 1, then G has a normal subgroup that is a direct product of t permutation groups of smaller degree that are either cyclic or doubly-transitive simple groups. As a consequence, we determine the full automorphism group of a Cayley digraph of an abelian group with two elementary divisors such that the Sylow p-subgroup of the full automorphism group is abelian.

Keywords


p-group, regular abelian subgroup, automorphism group

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DOI: https://doi.org/10.26493/1855-3974.70.960

ISSN: 1855-3974

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