HNN extensions of inverse semigroups and groupoids.
type: Item
instance of: scholarly article
title: HNN extensions of inverse semigroups and groupoids.
zbMATH Open document ID: 1041.20042
author: N. D. Gilbert
published in: Journal of Algebra
publication date: 2004-03-15T00:00:00Z
review text: In the category of groupoids HNN extensions have a natural definition modeled on the construction of a mapping torus. Properties of groupoid HNN extensions closely follow the properties of HNN extensions of groups, defined by \textit{G. Higman}, \textit{B. H. Neumann}, and \textit{H. Neumann} [J. Lond. Math. Soc. 24, 247-254 (1950; Zbl 0034.30101)]. In the paper under review the author uses the isomorphism between the categories of inverse semigroups and inductive groupoids to construct HNN extensions of inverse semigroups, where the associated inverse subsemigroups are order ideals of the base. Properties of groupoids then ensure that the base inverse semigroup always embeds in an HNN extension, constructed in this way. The author also describes the maximal subgroups, the maximal group image, and the structure of inverse subsemigroups generated by the stable letters in the HNN extensions. Several examples are discussed at the end of the paper.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 20M18
Mathematics Subject Classification ID: 20E06
zbMATH DE Number: 2057664
zbMATH Keywords: HNN extensions
zbMATH Keywords: categories of inverse semigroups
zbMATH Keywords: inductive groupoids
zbMATH Keywords: Higman-Neumann-Neumann embedding theorems for groups
describes a project that uses: Gpd
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2003.09.026
OpenAlex ID: W2007248682
cites work: Q3994461
cites work: Bass-Serre theory for groupoids and the structure of full regular semigroup amalgams
cites work: Amalgamation and Inverse and Regular Semigroups
cites work: The Fundamental Groupoid of a Graph of Groups
cites work: Embedding Theorems for Groups
cites work: EMBEDDING THEOREMS FOR SEMIGROUPS
cites work: The Word Problem for HNN-extensions of Free Inverse Semigroups
cites work: Almost factorisable inverse semigroups
cites work: Free Inverse Semigroups
cites work: Structure of regular semigroups. I
cites work: Q3473291
cites work: Q3341041
cites work: HNN Extensions of Inverse Semigroups and Applications
cites work: Locally full HNN extensions of inverse semigroups
DOI: 10.1016/J.JALGEBRA.2003.09.026
description: scientific article; zbMATH DE number 2057664