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Original Articles

One-Relator Products Induced from Generalized Triangle Groups

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Pages 2505-2526 | Received 01 Sep 2001, Accepted 01 May 2002, Published online: 18 Aug 2006
 

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.

Mathematics Subject Classification:

Acknowledgment

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

Notes

#Communicated by A. Olshanskii.

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