J Austral Math Soc Ser A 46 pp281--288, 1989.

Odd Order Groups with an Automorphism Cubing Many Elements

Marian Deaconescu and Desmond MacHale

(Received 3 July 1987; revised 27 January 1988)

Abstract

We determine the structure of a nonabelian group G of odd order such that some automorphism of G sends exactly (1/p)|G| elements to their cubes, where p is the smallest prime dividing |G|. These groups are close to being abelian in the sense that they either have nilpotency class 2 or have an abelian subgroup of index p.

1980 AMS Subject Classification (1985 Revision): 20E36

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Authors

Marian Deaconescu: Department of Mathematics, University of Timisoara, 1900-Timisoara, Romania.
Desmond MacHale: Department of Mathematics, University College, Cork, Ireland.

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Last Modified: Wed Feb 19 10:27:49 2003