Howson's property for semidirect products of semilattices by groups

2014/12/09 by Pedro V. Silva, Silva, Pedro V., Filipa Soares +1 · 1 citation
Computer Science · Mathematics · #20M18 #Computability, Logic, AI Algorithms #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1412.3048

openalex publication_date 2014/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An inverse semigroup S is a Howson inverse semigroup if the intersection of finitely generated inverse subsemigroups of S is finitely generated. Given a locally finite action θ of a group G on a semilattice E, it is proved that E ∗_θ G is a Howson inverse semigroup if and only if G is a Howson group. It is also shown that this equivalence fails for arbitrary actions.

Cited by

• Finitary conditions for graph products of monoids

Related

• Howson property and finitely generated intersection problem for monogenic inverse semigroups
• Howson groups which are not strongly Howson
• Some characterizations of Howson PC-groups
• On a groupoid construction for actions of certain inverse semigroups
• A remark on contracting inverse semigroups