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A characterisation of virtually free groups

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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.

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Authors and Affiliations

  1. Department of Mathematics, Stevens Institute of Technology, Hoboken, NJ, 07030, USA

    Robert H. Gilman

  2. Department of Mathematics, University of Nebraska, Lincoln, NE, 68588-0130, USA

    Susan Hermiller

  3. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

    Derek F. Holt

  4. School of Mathematics and Statistics, University of Newcastle, Newcastle, NE1 7RU, UK

    Sarah Rees

Authors
  1. Robert H. Gilman
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  2. Susan Hermiller
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  3. Derek F. Holt
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  4. Sarah Rees
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Corresponding author

Correspondence to Robert H. Gilman.

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Received: 30 October 2006

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Gilman, R.H., Hermiller, S., Holt, D.F. et al. A characterisation of virtually free groups. Arch. Math. 89, 289–295 (2007). https://doi.org/10.1007/s00013-007-2206-3

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  • DOI: https://doi.org/10.1007/s00013-007-2206-3

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