{"paper":{"title":"On a question of K\\\"ulshammer for representations of finite groups in reductive groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Benjamin Martin, Gerhard R\\\"ohrle, Michael Bate","submitted_at":"2015-05-02T22:42:04Z","abstract_excerpt":"Let $G$ be a simple algebraic group of type $G_2$ over an algebraically closed field of characteristic $2$. We give an example of a finite group $\\Gamma$ with Sylow $2$-subgroup $\\Gamma_2$ and an infinite family of pairwise non-conjugate homomorphisms $\\rho\\colon \\Gamma\\rightarrow G$ whose restrictions to $\\Gamma_2$ are all conjugate. This answers a question of Burkhard K\\\"ulshammer from 1995. We also give an action of $\\Gamma$ on a connected unipotent group $V$ such that the map of 1-cohomologies ${\\rm H}^1(\\Gamma,V)\\rightarrow {\\rm H}^1(\\Gamma_p,V)$ induced by restriction of 1-cocycles has a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00377","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"}