{"paper":{"title":"A classification of nilpotent 3-BCI groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Hiroki Koike, Istv\\'an Kov\\'acs","submitted_at":"2013-08-30T17:58:52Z","abstract_excerpt":"Given a finite group $G$ and a subset $S\\subseteq G,$ the bi-Cayley graph $\\bcay(G,S)$ is the graph whose vertex set is $G \\times \\{0,1\\}$ and edge set is $\\{\\{(x,0),(s x,1)\\} : x \\in G, s\\in S \\}$. A bi-Cayley graph $\\bcay(G,S)$ is called a BCI-graph if for any bi-Cayley graph $\\bcay(G,T),$ $\\bcay(G,S) \\cong \\bcay(G,T)$ implies that $T = g S^\\alpha$ for some $g \\in G$ and $\\alpha \\in \\aut(G)$. A group $G$ is called an $m$-BCI-group if all bi-Cayley graphs of $G$ of valency at most $m$ are BCI-graphs.In this paper we prove that, a finite nilpotent group is a 3-BCI-group if and only if it is in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6812","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"}