{"paper":{"title":"Non-abelian finite groups whose character sums are invariant but are not Cayley isomorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"A. Abdollahi, M. Zallaghi","submitted_at":"2017-10-12T11:03:14Z","abstract_excerpt":"Let $G$ be a group and $S$ an inverse closed subset of $G\\setminus \\{1\\}$. By a Cayley graph $Cay(G,S)$ we mean the graph whose vertex set is the set of elements of $G$ and two vertices $x$ and $y$ are adjacent if $x^{-1}y\\in S$. A group $G$ is called a CI-group if $Cay(G,S)\\cong Cay(G,T)$ for some inverse closed subsets $S$ and $T$ of $G\\setminus \\{1\\}$, then $S^\\alpha=T$ for some automorphism $\\alpha$ of $G$. A finite group $G$ is called a BI-group if $Cay(G,S)\\cong Cay(G,T)$ for some inverse closed subsets $S$ and $T$ of $G\\setminus \\{1\\}$, then $M_\\nu^S=M_\\nu^T$ for all positive integers $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04446","kind":"arxiv","version":1},"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"}