Generalized Baumslag–Solitar groups and geometric homomorphisms

A group is called a generalized Baumslag–Solitar group, or GBS-group, if it is the fundamental group of a graph of groups with infinite cyclic vertex and edge groups. A GBS-group is said to be GBS-simple if it has no proper, non-cyclic geometric quotients, i.e., quotients other than Z which arise fr...

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Bibliographic Details
Published in:Journal of pure and applied algebra 2011-04, Vol.215 (4), p.398-410
Main Authors: Delgado, Alberto L., Robinson, Derek J.S., Timm, Mathew
Format: Article
Language:English
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Summary:A group is called a generalized Baumslag–Solitar group, or GBS-group, if it is the fundamental group of a graph of groups with infinite cyclic vertex and edge groups. A GBS-group is said to be GBS-simple if it has no proper, non-cyclic geometric quotients, i.e., quotients other than Z which arise from geometric homomorphisms. The main result gives a complete description of the GBS-groups which are GBS-simple. This is achieved by constructing a set of natural examples of geometric homomorphisms.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2010.04.025