{"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 $G$. Moreover, we show that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04787","kind":"arxiv","version":3},"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"}