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These groups contain as special cases the odd dimensional general linear groups $GL_{2n+1}(R)$ where $R$ is any ring, the odd dimensional orthogonal and symplectic groups $O_{2n+1}(R)$ and $Sp_{2n+1}(R)$ where $R$ is any commutative ring and further the first author's even dimensional unitary groups $U_{2n}(R,\\Lambda)$ where $(R,\\Lambda)$ is any form ring. We classify the E-normal subgroups of the groups $U_{2n+1}(R,\\Delta)$ (i.e. the subgroups which are normalized by the elementary subgroup $EU_{2n+1}(R,\\Delta)$), un"},"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":"1506.08873","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2015-06-29T21:31:47Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"2f07cb965b9157c5d329d0e8b86ce6d2334da57b361fd17597657e8b68be7375","abstract_canon_sha256":"fcb5d8f73bbd65b7923cca3df1b71fca2dcdfe96a7dabda33095fb3e56311182"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:26.248871Z","signature_b64":"fx8EAUajc2kiGfIUPP8VSiPz9Aejx04/drJ9AK+mMRKgYcXuMbPWzkOFaY0HjlycHWSvn7EJ9U2bxGS45tOOCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc248903dc728d6553597591a24281efa70d7397a33af83941a8b18f6e87ae4b","last_reissued_at":"2026-05-18T00:32:26.248203Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:26.248203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The E-normal structure of odd dimensional unitary groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.KT","authors_text":"Anthony Bak, Raimund Preusser","submitted_at":"2015-06-29T21:31:47Z","abstract_excerpt":"In this paper we define odd dimensional unitary groups $U_{2n+1}(R,\\Delta)$. 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