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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
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Abstract

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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