{"paper":{"title":"Frobenius action on Carter subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"G\\\"ulin Ercan, \\.Ismail \\c{S}. G\\\"ulo\\u{g}lu","submitted_at":"2019-07-25T10:29:31Z","abstract_excerpt":"Let $G$ be a finite solvable group and $H$ be a subgroup of $Aut(G)$. Suppose that there exists an $H$-invariant Carter subgroup $F$ of $G$ such that the semidirect product $FH$ is a Frobenius group with kernel $F$. We prove that the terms of the Fitting series of $C_{G}(H)$ are obtained as the intersection of $C_{G}(H)$ with the corresponding terms of the Fitting series of $G$, and the Fitting height of $G$ may exceed the Fitting height of $C_{G}(H)$ by at most one. As a corollary it is shown that for any set of primes $\\pi$, the terms of the $\\pi$-series of $C_{G}(H)$ is obtained as the inte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.10951","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"}