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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Free $ E-m$ groups and free $ E-m$ semigroups


Author: Takayuki Tamura
Journal: Proc. Amer. Math. Soc. 84 (1982), 318-324
MSC: Primary 20M05; Secondary 20E05
MathSciNet review: 640222
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Abstract: A group [semigroup] is called $ E$-$ m$ if it satisfies the identity $ {(xy)^m} = {x^m}{y^m}$. In this paper the author studies a necessary and sufficient condition on $ m$ and $ n$ for the free $ E$-$ m$ group [semigroup] to be homomorphic onto the free $ E{\text{ - }}n$ group [semigroup].


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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0640222-7
PII: S 0002-9939(1982)0640222-7
Keywords: Free $ E{\text{ - }}m$ groups, free $ E{\text{ - }}m$ semigroups, exponent semigroups
Article copyright: © Copyright 1982 American Mathematical Society