On overgroups of regular abelian p-groups

Authors

  • Edward Dobson Mississippi State University, United States

DOI:

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

Keywords:

p-group, regular abelian subgroup, automorphism group

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.

Author Biography

Edward Dobson, Mississippi State University, United States

Associate Professor Department of Mathematics and Statistics Mississippi State University

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Published

2009-01-29

Issue

Vol. 2 No. 1 (2009)

Section

Articles

License

Articles in this journal are published under Creative Commons Attribution 4.0 International License
https://creativecommons.org/licenses/by/4.0/