On the number of subsemigroups of direct products involving the free\n monogenic semigroup

2018/03/21 by Ashley Clayton, Nik Ruškuc, Clayton, Ashley +1
Computer Science · #20M99 #FOS: Mathematics #Group Theory (math.GR) #Optimization and Search Problems #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1803.08091

openalex publication_date 2018/03/21 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

The direct product \ℕ\×\ℕ of two free monogenic\nsemigroups contains uncountably many pairwise non-isomorphic subdirect\nproducts. Furthermore, the following hold for \ℕ\× S, where S\nis a finite semigroup. It contains only countably many pairwise non-isomorphic\nsubsemigroups if and only if S is a union of groups. And it contains only\ncountably many pairwise non-isomorphic subdirect products if and only if every\nelement of S has a relative left- or right identity element.\n

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