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Denote by $\\mathrm{I}_{\\mathbb{F}_q}$ the augmentation ideal of the group ring $\\mathbb{F}_q[\\pi]$. We have found a surprising relation between the abelianization of $1+\\mathrm{I}_{\\mathbb{F}_q}$, the Bogomolov multiplier $\\mathrm{B}_0(\\pi)$ of $\\pi$ and the number of conjugacy classes $\\mathrm{k}(\\pi)$ of $\\pi$: \\[ | (1+\\mathrm{I}_{\\mathbb{F}_q})_{\\mathrm{ab}} |=q^{\\mathrm{k}(\\pi)-1}|\\mathrm{B}_0(\\pi)|. \\] In particular, if $\\pi$ is a finite $p$-group with a non-trivial Bogomolov multiplier, then $1+\\math","authors_text":"Andrei Jaikin-Zapirain, Javier Garcia-Rodriguez, Urban Jezernik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-02-11T10:15:18Z","title":"Units of group rings, the Bogomolov multiplier, and the fake degree conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03242","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3fc28bbfe6f3a249fd6f6b94c5655d259fc85de7d2a4984307c85e592a25a164","target":"record","created_at":"2026-05-18T02:27:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6fd3f8edda234fc9582a7c11445b5d8fa776efa86caf6d07ced984c0584a3c24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-02-11T10:15:18Z","title_canon_sha256":"2c03b37ef397e3722f606ac91f55465157f883315214e0211fee92ff4c65087d"},"schema_version":"1.0","source":{"id":"1502.03242","kind":"arxiv","version":1}},"canonical_sha256":"7c3d5e93cf7e52e28087868e3c6ef046bb56deb4395821320c1dcbc1f7d30443","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c3d5e93cf7e52e28087868e3c6ef046bb56deb4395821320c1dcbc1f7d30443","first_computed_at":"2026-05-18T02:27:20.045224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:20.045224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NS6G5Ze+jl4mP1HTE87ga3g9OuGhpe2xWdjvBeH4HQNp77M2n4iTd11I+fVoeXptL7pvu21LU7qinRSeau2ACw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:20.046050Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.03242","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fc28bbfe6f3a249fd6f6b94c5655d259fc85de7d2a4984307c85e592a25a164","sha256:9de6151dec56ada3f0204529c9af327adbe6f03015f28ce61c8bc75c174d918d"],"state_sha256":"24c4da7f9467dd157305ca05d0fb21326312b503c8cf7afc8eea7b6a3db0d36b"}