Generators and relations for subsemigroups via boundaries in Cayley graphs

被引：2

作者：

Gray, R. ^{[1
]}

Ruskuc, N. ^{[2
]}

机构：

[1] Univ Lisbon, Ctr Algebra, P-1649003 Lisbon, Portugal

[2] Univ St Andrews, Sch Math & Stat, St Andrews KY16 9SS, Fife, Scotland

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2011年 / 215卷 / 11期

基金：

英国工程与自然科学研究理事会;

关键词：

METABELIAN-GROUPS; SPECIAL MONOIDS; SEMIGROUPS; SUBGROUPS; PRESENTATIONS; INDEX;

D O I：

10.1016/j.jpaa.2011.03.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a finitely generated semigroup S and subsemigroup T of S. we define the notion of the boundary of T in S which, intuitively, describes the position of T inside the left and right Cayley graphs of S. We prove that if S is finitely generated and T has a finite boundary in S then T is finitely generated. We also prove that if S is finitely presented and T has a finite boundary in S then T is finitely presented. Several corollaries and examples are given. (C) 2011 Elsevier B.V. All rights reserved.

引用

页码：2761 / 2779

页数：19

共 29 条

[1]

[Anonymous], 1989, CAMBRIDGE STUD ADV M

[2] On generators and relations for unions of semigroups [J].