A characterisation of virtually free groups

Robert H. Gilman; Susan Hermiller; Derek F. Holt; Sarah Rees

doi:10.1007/s00013-007-2206-3

A characterisation of virtually free groups

Robert H. Gilman
, Susan Hermiller
, Derek F. Holt
, Sarah Rees

Department of Mathematical Sciences

University of Nebraska-Lincoln
University of Warwick
Newcastle University

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

20 Scopus citations

Abstract

We prove that a finitely generated group G is virtually free if and only if there exists a generating set for G and k > 0 such that all k-locally geodesic words with respect to that generating set are geodesic.

Original language	English
Pages (from-to)	289-295
Number of pages	7
Journal	Archiv der Mathematik
Volume	89
Issue number	4
DOIs	https://doi.org/10.1007/s00013-007-2206-3
State	Published - Oct 2007

Keywords

Dehn algorithm
Virtually free group
Word problem

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title = "A characterisation of virtually free groups",

abstract = "We prove that a finitely generated group G is virtually free if and only if there exists a generating set for G and k > 0 such that all k-locally geodesic words with respect to that generating set are geodesic.",

keywords = "Dehn algorithm, Virtually free group, Word problem",

author = "Gilman, \{Robert H.\} and Susan Hermiller and Holt, \{Derek F.\} and Sarah Rees",

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T1 - A characterisation of virtually free groups

AU - Gilman, Robert H.

AU - Hermiller, Susan

AU - Holt, Derek F.

AU - Rees, Sarah

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N2 - We prove that a finitely generated group G is virtually free if and only if there exists a generating set for G and k > 0 such that all k-locally geodesic words with respect to that generating set are geodesic.

AB - We prove that a finitely generated group G is virtually free if and only if there exists a generating set for G and k > 0 such that all k-locally geodesic words with respect to that generating set are geodesic.

KW - Dehn algorithm

KW - Virtually free group

KW - Word problem

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DO - 10.1007/s00013-007-2206-3

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VL - 89

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EP - 295

JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 4

ER -

A characterisation of virtually free groups

Abstract

Keywords

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