On the number of countable subdirect powers of finite commutative semigroups

2022/08/31 by Ashley Clayton, Nik Ruškuc, Clayton, Ashley +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2208.14854

openalex publication_date 2022/08/31 · openalex created_date 2022/09/03 · openalex updated_date 2026/07/28

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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