Cyclic normal subgroups of generalized Baumslag–Solitar groups |
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Authors: | Alberto L Delgado Mathew Timm |
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Institution: | 1. Department of Mathematics, Illinois State University, Normal, Illinois, USA;2. Department of Mathematics, Bradley University, Peoria, Illinois, USA |
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Abstract: | The centers and cyclic radicals of generalized Baumslag–Solitar groups (GBS-groups) are studied. Criteria for their non-triviality are found and an algorithm to compute the center and cyclic radical is given. In addition, for each unimodular GBS-group, a GBS-cover, i.e., a GBS-group in whose underlying graph the weights around each vertex are constant in absolute value, is constructed. These groups are then characterized by a minimality property. |
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Keywords: | Covering group cyclic radical generalized Baumslag–Solitar group |
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