{"paper":{"title":"A class of 2-groups admitting an action of the symmetric group of degree 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Kieran Roberts, Sergey Shpectorov","submitted_at":"2013-01-02T19:04:34Z","abstract_excerpt":"A biextraspecial group of rank $m$ is an extension of a special 2-group $Q$ of the form $2^{2 + 2m}$ by $L\\cong L_2(2)$, such that the 3-element from $L$ acts on $Q$ fixed-point-freely. Subgroups of this type appear in at least the sporadic groups $J_2$, $J_3$, $McL$, $Suz$, and $Co_1$. In this paper we completely classify biextraspecial groups, namely, we show that the rank $m$ must be even and for each such $m$ there exist exactly two biextraspecial groups $B^\\varepsilon(m)$ up to isomorphism where $\\varepsilon\\in{+,-}$. We also prove that $\\Out(B^\\varepsilon(m))$ is an extension of the $m$-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0292","kind":"arxiv","version":2},"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"}