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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1704.09013","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-04-28T17:17:51Z","cross_cats_sorted":["math.DS","math.OA","math.RT"],"title_canon_sha256":"a7510bf9990f04bc2790cd72232c1352365aae0b0c4559e4891eefe151500670","abstract_canon_sha256":"3dc448917da5cad309251ddd9f2eeb9f3db701c16312fa5d0318d71d90d40e68"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:30.639949Z","signature_b64":"h5/a+qwFWcwGqyf5fUkRqecsfcYED5UU7SLcCnr4zWMV7j2Hp0DRoVImVox85owxkqY2fDTLCUn2nFUg1oG2AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41f7ffb4fd4b100d9aecc3bb092fdb2d1020afd0a30a898826aaf0a9d9640b9b","last_reissued_at":"2026-05-18T00:19:30.639444Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:30.639444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $G$. 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