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We review the known weaker versions of this conjecture and introduce a new condition, on the partial augmentations of the powers of a unit of finite order in $\\mathbb{Z}G$, which is weaker than the Zassenhaus Conjecture but stronger than its other weaker versions.\n  We prove that this condition is satisfied for units mapping to the identity modulo a nilpotent normal subgroup of $G$. Moreover, we show that"},"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":"1706.04787","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-06-15T09:16:35Z","cross_cats_sorted":["math.GR","math.RT"],"title_canon_sha256":"b5740ffa374461fd7b518dba0a2d5be862a70e87d8d6e030d14afdc1d197d9a5","abstract_canon_sha256":"54fd28dab9b5320c3f8f757506958797dcc644bbccd524ee9d860ddac0551ab3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:43.871811Z","signature_b64":"oDN7fHIb5mpFI4kYfSOh6rdUqOEN8KEsyoqY1hTceBd9Ekg3zBOC840zZeILQ1qM3aENlJL75G+enUZcWsn4Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7cc3109522c2d9b53b63407e2b728d8f7de58fbb6dcee657fa35c448752de6f","last_reissued_at":"2026-05-18T00:01:43.871273Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:43.871273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Partial Augmentations Power property: A Zassenhaus Conjecture related problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.RA","authors_text":"\\'Angel del R\\'io, Leo Margolis","submitted_at":"2017-06-15T09:16:35Z","abstract_excerpt":"Zassenhaus conjectured that any unit of finite order in the integral group ring $\\mathbb{Z}G$ of a finite group $G$ is conjugate in the rational group algebra of $G$ to an element in $\\pm G$. We review the known weaker versions of this conjecture and introduce a new condition, on the partial augmentations of the powers of a unit of finite order in $\\mathbb{Z}G$, which is weaker than the Zassenhaus Conjecture but stronger than its other weaker versions.\n  We prove that this condition is satisfied for units mapping to the identity modulo a nilpotent normal subgroup of $G$. 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