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A characterisation of virtually free groups

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

Publisher
Springer
Year
2007
Tongue
English
Weight
130 KB
Volume
89
Category
Article
ISSN
0003-889X

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✦ Synopsis

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

πŸ“œ SIMILAR VOLUMES

A simple construction of virtually free
A simple construction of virtually free Abelian triangles of finite groups
✍ Paul R. Brown πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 44 KB

A virtually torsion free, non-positively curved polygon of finite groups has virtual cohomological dimension two. In this paper, the assumption of non-positive curvature is dropped, and a simple construction is used to obtain a triangle of finite groups which is virtually Z k , 2 < k < ∞.