{"title":"On the structure of lower bounded HNN extensions","authors":"Paul Bennett, T. Jajcayová","doi":"10.1017/S001708952300023X","DOIUrl":null,"url":null,"abstract":"Abstract This paper studies the structure and preservational properties of lower bounded HNN extensions of inverse semigroups, as introduced by Jajcayová. We show that if \n$S^* = [ S;\\; U_1,U_2;\\; \\phi ]$\n is a lower bounded HNN extension then the maximal subgroups of \n$S^*$\n may be described using Bass-Serre theory, as the fundamental groups of certain graphs of groups defined from the \n$\\mathcal{D}$\n -classes of \n$S$\n , \n$U_1$\n and \n$U_2$\n . We then obtain a number of results concerning when inverse semigroup properties are preserved under the HNN extension construction. The properties considered are completely semisimpleness, having finite \n$\\mathcal{R}$\n -classes, residual finiteness, being \n$E$\n -unitary, and \n$0$\n - \n$E$\n -unitary. Examples are given, such as an HNN extension of a polycylic inverse monoid.","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":"65 1","pages":"697 - 715"},"PeriodicalIF":0.5000,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Glasgow Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/S001708952300023X","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract This paper studies the structure and preservational properties of lower bounded HNN extensions of inverse semigroups, as introduced by Jajcayová. We show that if
$S^* = [ S;\; U_1,U_2;\; \phi ]$
is a lower bounded HNN extension then the maximal subgroups of
$S^*$
may be described using Bass-Serre theory, as the fundamental groups of certain graphs of groups defined from the
$\mathcal{D}$
-classes of
$S$
,
$U_1$
and
$U_2$
. We then obtain a number of results concerning when inverse semigroup properties are preserved under the HNN extension construction. The properties considered are completely semisimpleness, having finite
$\mathcal{R}$
-classes, residual finiteness, being
$E$
-unitary, and
$0$
-
$E$
-unitary. Examples are given, such as an HNN extension of a polycylic inverse monoid.
期刊介绍:
Glasgow Mathematical Journal publishes original research papers in any branch of pure and applied mathematics. An international journal, its policy is to feature a wide variety of research areas, which in recent issues have included ring theory, group theory, functional analysis, combinatorics, differential equations, differential geometry, number theory, algebraic topology, and the application of such methods in applied mathematics.
The journal has a web-based submission system for articles. For details of how to to upload your paper see GMJ - Online Submission Guidelines or go directly to the submission site.