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Isaacs constructed a natural correspondence between the set Irr_A(N) of irreducible complex characters invariant under the action of A, and the irreducible characters of the centralizer of A in N, Irr(C_N(A)). We show that this correspondence preserves Schur indices over the rational numbers. Moreover, suppose that the semidirect product AN is a normal subgroup of the finite group G and set U= N_G(A). Let \\chi \\in Irr_A(N) and \\chi* \\in Irr(C_N(A)) correspond. Then there is a c"},"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":"1108.3777","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-08-18T15:31:09Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"6fa872cb95dc9aa748bbc5ceb4d3ba9be544f3e5ff991bc967810affc681885a","abstract_canon_sha256":"5277270f805fae637da0f123e1b1fd5e4e1d415570e5760a104eb3d40635a76a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:07.480254Z","signature_b64":"4GFK8zNQCGrcZwB8RLxMqbHza0uiLtjh5nw79HGtSjKMAXF5TgujCfRQJHq0R1zkcjbKWa520qKbupwQ1YgqBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c6fb9bb74a60676b66e131d4c0489ba39cc4db7447367d8586961858d0f8451","last_reissued_at":"2026-05-18T04:15:07.479560Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:07.479560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Character correspondences above fully ramified sections and Schur indices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Frieder Ladisch","submitted_at":"2011-08-18T15:31:09Z","abstract_excerpt":"Let N be a finite group of odd order and A a finite group that acts on N such that the orders of N and A are coprime. Isaacs constructed a natural correspondence between the set Irr_A(N) of irreducible complex characters invariant under the action of A, and the irreducible characters of the centralizer of A in N, Irr(C_N(A)). We show that this correspondence preserves Schur indices over the rational numbers. Moreover, suppose that the semidirect product AN is a normal subgroup of the finite group G and set U= N_G(A). Let \\chi \\in Irr_A(N) and \\chi* \\in Irr(C_N(A)) correspond. 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