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It is proved that $G$ has a characteristic soluble subgroup of derived length bounded in terms of $n,c$ whose index is bounded in terms of $m,n,c$. A similar result is also proved for Lie rings."},"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":"1409.7807","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-09-27T12:45:04Z","cross_cats_sorted":[],"title_canon_sha256":"5563e5636bd1fb10b088019d3048f8067f49a07ba9dcbad36fda3bf49e1418b8","abstract_canon_sha256":"7e34ad63db4e75a9244bbe18e19db10767f305b3224c44b980d988bf220d0b67"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:40.805304Z","signature_b64":"Jm0RAFfoSDtQW0XtohVCdFwv0rXYMvN8yoioVV3iG0Hd1VgIUpIXhoYqm/fuAc1GqR33YKm7s63AgZTFmGk6Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f3a4a9eb25e14606138f275d8f701ab2984af252df43076eac1359fb501f94c","last_reissued_at":"2026-05-18T02:18:40.804600Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:40.804600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite groups and Lie rings with an automorphism of order $2^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"E. I. Khukhro, N. Yu. Makarenko, P. Shumyatsky","submitted_at":"2014-09-27T12:45:04Z","abstract_excerpt":"Suppose that a finite group $G$ admits an automorphism $\\varphi $ of order $2^n$ such that the fixed-point subgroup $C_G(\\varphi ^{2^{n-1}})$ of the involution $\\varphi ^{2^{n-1}}$ is nilpotent of class $c$. Let $m=|C_G(\\varphi)|$ be the number of fixed points of $\\varphi$. It is proved that $G$ has a characteristic soluble subgroup of derived length bounded in terms of $n,c$ whose index is bounded in terms of $m,n,c$. 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