{"paper":{"title":"Cardinal invariants distinguishing permutation groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.LO"],"primary_cat":"math.GR","authors_text":"Heike Mildenberger, Taras Banakh","submitted_at":"2015-06-30T07:35:49Z","abstract_excerpt":"We prove that for infinite cardinals $\\kappa<\\lambda$ the alternating group $Alt(\\lambda)$ (of even permutations) of $\\lambda$ is not embeddable into the symmetric group $Sym(\\kappa)$ (of all permutations) of $\\kappa$. To prove this fact we introduce and study several monotone cardinal group invariants which take value $\\kappa$ on the groups $Alt(\\kappa)$ and $Sym(\\kappa)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08969","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"}