Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-06-16T23:13:28.181Z Has data issue: false hasContentIssue false
  • English
  • Français

A Characterization of the Commutator Subgroup of a Group

Published online by Cambridge University Press:  20 November 2018

G. Thierrin
G. Thierrin*
Affiliation:
Department of Mathematics, University of Western Ontario, London, Ontario, CanadaN6A 3K7
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An element a of a semigroup S is n-potent if there exist a1, a2,..., ak∈S such that a = a1a2...ak and If S is a group, the set of n-potent elements is a normal subgroup of S and the set of 1-potent elements is the commutator subgroup of S.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 1 , 01 March 1976 , pp. 93 - 94
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vol. 2, Math. Survey 7, Amer. Math. Soc. 1967.Google Scholar
2. Howie, J. M., The subsemigroup generated by the idempotents of a full transformation semigroup, J. London Math. Soc. 41, 1966, 707–716.Google Scholar