{"paper":{"title":"Absorption of Direct Factors With Respect to the Minimal Faithful Permutation Degree of a Finite Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"David Easdown, Michael Hendriksen, Neil Saunders","submitted_at":"2016-10-17T20:17:20Z","abstract_excerpt":"The minimal faithful permutation degree $\\mu(G)$ of a finite group $G$ is the least nonnegative integer $n$ such that $G$ embeds in the symmetric group $\\Sym(n)$. We prove that if $H$ is a group then $\\mu(G)=\\mu(G\\times H)$ for some group $G$ then $H$ embeds in $A\\times Q^k$ for some abelian group of odd order, some generalised quaternion $2$-group and some nonnegative integer $k$. As a consequence, $\\mu(G^{n+1})=\\mu(G^n)$ for some nonnegative integer $n$ if and only if $G$ is trivial."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05336","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"}