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arXiv · 2208.14854

On the number of countable subdirect powers of finite commutative semigroups

Ashley Clayton·Nik Ruskuc
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Abstract

In 1981/82, Hickin \& Plotkin and McKenzie both proved that a finite group has only countably many non-isomorphic subdirect powers if and only if it is abelian. In this paper, we prove that a finite commutative semigroup has only countably many non-isomorphic countable subdirect powers if and only if it is either a finite abelian group or a null semigroup.

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Ashley Clayton, Nik Ruskuc. 2022-08-31. On the number of countable subdirect powers of finite commutative semigroups. https://arxiv.org/abs/2208.14854

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