One-Relator Products Induced from Generalized Triangle Groups

Abstract

We study the quotient of a free product of groups by the normal closure of a word that is contained in a certain type of 2-generator subgroup, and hence can be expressed in the form of a pushout involving a generalized triangle group. Using the theory of generalized triangle groups, we extend the range of conditions under which a number of results for one-relator products of groups, such as the Freiheitssatz and the solubility of the word problem, are known to hold.

Key Words:

• One-relator
• Freiheitssatz
• Word problem
• Generalized triangle group

Mathematics Subject Classification:

• Primary 20F05
• Secondary 20F10, 57M07

Acknowledgment

The second author was supported by Marie Curie Fellowship no. HPMF-CT-1999-00172.

Notes

^#Communicated by A. Olshanskii.