Splittings of generalized Baumslag-Solitar groups

Details Splittings of generalized Baumslag-Solitar groups Splittings of generalized Baumslag-Solitar groups

2005-02-02

arxiv.org/abs/math/0502060v2

Mathematics

Group Theory

20 pages; hyperlinked latex. Version 2: minor changes

Scientific paper

We study the structure of generalized Baumslag-Solitar groups from the point of view of their (usually non-unique) splittings as fundamental groups of graphs of infinite cyclic groups. We find and characterize certain decompositions of smallest complexity (`fully reduced' decompositions) and give a simplified proof of the existence of deformations. We also prove a finiteness theorem and solve the isomorphism problem for generalized Baumslag-Solitar groups with no non-trivial integral moduli.

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