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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1907.10951","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-07-25T10:29:31Z","cross_cats_sorted":[],"title_canon_sha256":"efba9041d77e1b1051fc2171acb95da1a686b892cb59a281fdf1bef1ce354692","abstract_canon_sha256":"aaa4bbbcbc7eceab9b2ad659c919eec9967dc63c8fb42257ae2dc6a75aceeb1a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:33.935263Z","signature_b64":"JE+3Wgslceut1S7+UoRjML18tBTpFG+4DVfniJ+36hB/B+fUIeuPshAPZZyjrZZ2g6QDHhcAHIGDuZA+4LfmBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77cf0f0368a3e9aaa5d00f15ca5374bc2fa6ba2a5c53fd8c8ee8b6e3dccc45fa","last_reissued_at":"2026-05-17T23:39:33.934627Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:33.934627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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