One-relator products induced from generalized triangle groups

James Howie; Robert Shwartz

doi:10.1081/AGB-120037396

One-relator products induced from generalized triangle groups

James Howie, Robert Shwartz

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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
Pages (from-to)	2505-2526
Number of pages	22
Journal	Communications in Algebra
Volume	32
Issue number	7
DOIs	https://doi.org/10.1081/AGB-120037396
State	Published - 2004
Externally published	Yes

Keywords

Freiheitssatz
Generalized triangle group
One-relator
Word problem

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10.1081/AGB-120037396

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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.",

keywords = "Freiheitssatz, Generalized triangle group, One-relator, Word problem",

author = "James Howie and Robert Shwartz",

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AB - 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.

KW - Freiheitssatz

KW - Generalized triangle group

KW - One-relator

KW - Word problem

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JO - Communications in Algebra

JF - Communications in Algebra

IS - 7

ER -

One-relator products induced from generalized triangle groups

Abstract

Keywords

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