On the residual finiteness and other properties of (relative) one-relator groups

Pride, S. (2006) On the residual finiteness and other properties of (relative) one-relator groups. In: Geometric Methods in Group Theory, Ottawa, Canada, 16-19 August 2006,

Abstract

A relative one-relator presentation has the form P = (X, H ; R) where X is a set, H is a group, and R is a group word on X and H. We show that if the group word on X obtained from R by deleting all the terms from H has what we call the unique max-min property, then the group defined by P is residually finite if and only if H is residually finite (Theorem 1). We apply this to obtain new results concerning the residual finiteness of (ordinary) one-relator groups (Theorem 4). We also obtain results concerning the conjugacy problem for one-relator groups (Theorem 5), and results concerning the relative asphericity of presentations of the form P (Theorem 6).

• Item Type: Conference Proceedings
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Pride, Professor Stephen
• Authors: Pride, S.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics