On the retractability of some one-relator groups

Richard Dowell Byrd, Justin Thomas Lloyd and Roberto A. Mena

Vol. 72 (1977), No. 2, 351–359

DOI: 10.2140/pjm.1977.72.351

Abstract

Recently the concept of a retractable group has been introduced. This class of groups contains the class of lattice-ordered groups as a proper subclass, and, in particular, contains the class of all torsion-free abelian groups. Retractable groups enjoy many of the properties of lattice-ordered groups; in fact, most results concerning lattice-ordered groups have immediate extensions to this wider class. In this note, we investigate the retractability of certain two-generator one-relator groups.

Mathematical Subject Classification 2000

Primary: 20F05

Milestones

Received: 11 June 1976

Revised: 21 April 1977

Published: 1 October 1977