Free 𝐸-𝑚 groups and free 𝐸-𝑚 semigroups

Tamura, Takayuki

doi:10.1090/S0002-9939-1982-0640222-7

Free $E-m$ groups and free $E-m$ semigroups
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by Takayuki Tamura

Proc. Amer. Math. Soc. 84 (1982), 318-324

DOI: https://doi.org/10.1090/S0002-9939-1982-0640222-7

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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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