Generalized Baumslag–Solitar groups and geometric homomorphisms

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• 作者：Alberto L. Delgado ; Derek J.S. Robinson ; Mathew Timm
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2011
• 出版时间：April 2011
• 年：2011
• 卷：215
• 期：4
• 页码：398-410
• 全文大小：677 K

文摘

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 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.