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Odd order groups with an automorphism cubing many elements

Part of: Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

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

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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.

MSC classification

Secondary: 20E36: Automorphisms of infinite groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 2 , April 1989 , pp. 281 - 288
Copyright
Copyright © Australian Mathematical Society 1989

References

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