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Groups in which Raising to a Power is an Automorphism

Published online by Cambridge University Press:  20 November 2018

H. F. Trotter
H. F. Trotter*
Affiliation:
Princeton University
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For any group G and integer n, let Pn:G→G be the function defined by Pn(g) = gn for all g ϵ G. If G is abelian then Pn is a homomorphism for all n. Conversely, it is well known (and easy to show) that if P2 or P-1 is a homomorphism then G is abelian. As the groups Gn described below show, for every n other than 2 and -1 there exist non-abelian groups for which Pn is a homomorphism.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 6 , December 1965 , pp. 825 - 827
Copyright
Copyright © Canadian Mathematical Society 1965