On the number of countable subdirect powers of finite commutative semigroups
Group Theory
2022-09-01 v1
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.
Keywords
Cite
@article{arxiv.2208.14854,
title = {On the number of countable subdirect powers of finite commutative semigroups},
author = {Ashley Clayton and Nik Ruskuc},
journal= {arXiv preprint arXiv:2208.14854},
year = {2022}
}
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12 pages