{"paper":{"title":"The Smallest Faithful Permutation Degree for a Direct Product Obeying an Inequality Condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"David Easdown, Neil Saunders","submitted_at":"2014-10-29T01:25:41Z","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 $\\Sym(n)$. Clearly $\\mu(G \\times H) \\le \\mu(G) + \\mu(H)$ for all finite groups $G$ and $H$. Wright (1975) proves that equality occurs when $G$ and $H$ are nilpotent and exhibits an example of strict inequality where $G\\times H$ embeds in $\\Sym(15)$.\n  Saunders (2010) produces an infinite family of examples of permutation groups $G$ and $H$ where $\\mu(G \\times H) < \\mu(G) + \\mu(H)$, including the example of Wright's as a special case. The smalle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7854","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"}