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On Canonical Generators of Subgroups

Published online by Cambridge University Press:  20 November 2018

Peter Fantham
Peter Fantham*
Affiliation:
University of Toronto, Toronto, Ontario
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Let H be a cyclic group, K⊂H a subgroup and x, y generators of H, K. We shall say that x, y are related if y=xa where a is the index of K in H, in other words, y is the smallest positive power of x in K. The main purpose of this note is to show that for any group G one may, by means of the axiom of choice, choose for each cyclic group H⊂G a generator xH such that when K⊂H then xK, xH are related.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 3 , September 1971 , pp. 321 - 323
Copyright
Copyright © Canadian Mathematical Society 1971