The product formula for Reidemeister numbers on nilpotent groups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915167954010112 |
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| author | Senden, Pieter |
| author_facet | Senden, Pieter |
| contents | We study the product formula for Reidemeister numbers on finitely generated torsion-free nilpotent groups in two ways. On the one hand, we generalise the product formula to central extensions. On the other hand, we derive general results for finitely generated (torsion-free) nilpotent groups from the product formula: we provide a strong tool to prove that an endomorphism on a finitely generated nilpotent group has infinite Reidemeister number and compute Reidemeister numbers on finite index subgroups of finitely generated torsion-free nilpotent groups. Using the latter, we provide an infinite family of groups with full Reidemeister spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16651 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The product formula for Reidemeister numbers on nilpotent groups Senden, Pieter Group Theory 20E45, 20F18 (Primary) 20E22 (Secondary) We study the product formula for Reidemeister numbers on finitely generated torsion-free nilpotent groups in two ways. On the one hand, we generalise the product formula to central extensions. On the other hand, we derive general results for finitely generated (torsion-free) nilpotent groups from the product formula: we provide a strong tool to prove that an endomorphism on a finitely generated nilpotent group has infinite Reidemeister number and compute Reidemeister numbers on finite index subgroups of finitely generated torsion-free nilpotent groups. Using the latter, we provide an infinite family of groups with full Reidemeister spectrum. |
| title | The product formula for Reidemeister numbers on nilpotent groups |
| topic | Group Theory 20E45, 20F18 (Primary) 20E22 (Secondary) |
| url | https://arxiv.org/abs/2502.16651 |