{"paper":{"title":"Twisted Burnside-Frobenius theory for endomorphisms of polycyclic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.OA","math.RT"],"primary_cat":"math.GR","authors_text":"Alexander Fel'shtyn, Evgenij Troitsky","submitted_at":"2017-04-28T17:17:51Z","abstract_excerpt":"Let $R(\\phi)$ be the number of $\\phi$-conjugacy (or Reidemeister) classes of an endomorphism $\\phi$ of a group $G$. We prove for several classes of groups (including polycyclic) that the number $R(\\phi)$ is equal to the number of fixed points of the induced map of an appropriate subspace of the unitary dual space $\\widehat G$, when $R(\\phi)<\\infty$. Applying the result to iterations of $\\phi$ we obtain Gauss congruences for Reidemeister numbers.\n  In contrast with the case of automorphisms, studied previously, we have a plenty of examples having the above finiteness condition, even among group"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.09013","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}