Full paper in PDF:
$%B. Fine, G. Rosenberger, and M. Stille, Conjugacy pinched and cyclically pinched one-relator groups, Rev. Mat. Univ. Complut. Madrid 10 (1997), no. 2, 207–227.%$

Conjugacy Pinched and Cyclically Pinched One-Relator Groups
Benjamin FINE, Gerhard ROSENBERGER,
and Michael STILLE
Department of Mathematics
Fairfield University
Fairfield, Connecticut 06430 — USA
Fachbereich Mathematik Universität
44221 Dortmund — F.R. Germany

Received: March 10, 1997
Revised: June 15, 1997
ABSTRACT

Here we consider two classes of torsion-free one-relator groups which have proved quite amenable to study-the cyclically pinched one-relator groups and the conjugacy pinched one-relator groups. The former is the class of groups which are free products of free groups with cyclic amalgamations while the latter is the class of HNN extensions of free groups with cyclic associated subgroups. Both are generalizations of surface groups. We compare and contrast results in these classes relative to n -freeness, separability properties including conjugacy separability, subgroup separability and residual finiteness, decision theoretic properties including the isomorphism problem and hyperbolicity.

1991 Mathematics Subject Classification: 20E05, 20E06, 20E07.