{"paper":{"title":"Automorphism group of the complete alternating group graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Qiongxiang Huang, Xueyi Huang","submitted_at":"2016-05-21T16:03:50Z","abstract_excerpt":"Let $S_n$ and $A_n$ denote the symmetric group and alternating group of degree $n$ with $n\\geq 3$, respectively. Let $S$ be the set of all $3$-cycles in $S_n$. The \\emph{complete alternating group graph}, denoted by $CAG_n$, is defined as the Cayley graph $\\mathrm{Cay}(A_n,S)$ on $A_n$ with respect to $S$. In this paper, we show that $CAG_n$ ($n\\geq 4$) is not a normal Cayley graph. Furthermore, the automorphism group of $CAG_n$ for $n\\geq 5$ is obtained, which equals to $\\mathrm{Aut}(CAG_n)=(R(A_n)\\rtimes \\mathrm{Inn}(S_n))\\rtimes \\mathbb{Z}_2\\cong (A_n\\rtimes S_n)\\rtimes \\mathbb{Z}_2$, where"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06664","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"}