{"paper":{"title":"On the distribution of conjugacy classes between the cosets of a finite group in a cyclic extension","license":"","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"John R. Britnell, Mark Wildon","submitted_at":"2007-09-01T14:01:21Z","abstract_excerpt":"Let G be a finite group and H a normal subgroup such that G/H is cyclic. Given a conjugacy class g^G of G we define its centralizing subgroup to be HC_G(g). Let K be such that H\\le K\\le G. We show that the G-conjugacy classes contained in K whose centralizing subgroup is K, are equally distributed between the cosets of H in K. The proof of this result is entirely elementary. As an application we find expressions for the number of conjugacy classes of K under its own action, in terms of quantities relating only to the action of G."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.0064","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"}