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.
Original language | English |
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Pages (from-to) | 2505-2526 |
Number of pages | 22 |
Journal | Communications in Algebra |
Volume | 32 |
Issue number | 7 |
DOIs | |
State | Published - 2004 |
Externally published | Yes |
Keywords
- Freiheitssatz
- Generalized triangle group
- One-relator
- Word problem