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On overgroups of regular abelian p-groups
Let â–«â–« be a transitive group of odd prime-power degree whose Sylow â–«â–«-subgroup â–«â–« is abelian od rank â–«â–«. Weshow that if â–«â–«, then â–«â–« has a normal subgroup that is a direct product of â–«â–« 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 diagraph of an abelian group with rank two such that the Sylow â–«â–«-subgroup of the full automorphism group is abelian
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