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Using some arguments of Hamidoune, we establish an analogue in the noncommutative setting. Namely, if $A$ is a finite non-empty subset of a nonabelian group $G = (G,\\cdot)$ such that $|A \\cdot A| \\leq (2-\\eps) |A|$, then $A$ is either contained in a right-coset of a finite group $H$ of cardinality at most $\\frac{2}{\\eps}|A|$, or can be co"},"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":"1106.2267","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-11T23:24:03Z","cross_cats_sorted":[],"title_canon_sha256":"a83e367d5a77aa66bea6a5030aa4205c63c90de3f08eda52185970d19cd88959","abstract_canon_sha256":"96897bfb5cc0c9ff043744314f156fae3198d65fdbc60119aca504358d07e0c1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:48.735578Z","signature_b64":"ZwDYDJwaf4nWtMV67zhwmIrQFAKSiqEsegi3CjVmnuuN74iCefD2wvkKz++H7uTxn9+p9FE0VnTL7kg5ETiXBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e82f28cead331e755bb2e1fa2ffb9530c6ceb842037b95dc00d7c4935f0281b","last_reissued_at":"2026-05-18T03:58:48.735063Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:48.735063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Noncommutative sets of small doubling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Terence Tao","submitted_at":"2011-06-11T23:24:03Z","abstract_excerpt":"A corollary of Kneser's theorem, one sees that any finite non-empty subset $A$ of an abelian group $G = (G,+)$ with $|A + A| \\leq (2-\\eps) |A|$ can be covered by at most $\\frac{2}{\\eps}-1$ translates of a finite group $H$ of cardinality at most $(2-\\eps)|A|$. 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