{"paper":{"title":"Variations on the Baer--Suzuki Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Gunter Malle, Robert Guralnick","submitted_at":"2013-10-22T13:19:33Z","abstract_excerpt":"The Baer--Suzuki theorem says that if $p$ is a prime, $x$ is a $p$-element in a finite group $G$ and $\\langle x, x^g \\rangle$ is a $p$-group for all $g \\in G$, then the normal closure of $x$ in $G$ is a $p$-group. We consider the case where $x^g$ is replaced by $y^g$ for some other $p$-element $y$. While the analog of Baer--Suzuki is not true, we show that some variation is. We also answer a closely related question of Pavel Shumyatsky on commutators of conjugacy classes of $p$-elements."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5909","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"}