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We say that $G$ is \\emph{weakly rectangular} if there are finite subsets $F_i\\subseteq \\mathbb{N}$ and subgroups $H_i$ of $\\bigoplus\\limits_{j\\in F_i} G_j$ that satisfy $G=\\prod\\limits_{i\\in\\mathbb{N}}H_i$. %We say that $G$ is a \\emph{subdirect product} of the family $\\{G_i\\}_{i\\in I}$ if $G$ is weakly rectangular and %$G\\cap\\bigoplus\\limits_{i\\in I} G_i=\\bigoplus\\limits_{i\\in\\mathbb{N}}H_i$. In this paper we discuss when a c"},"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":"1811.08171","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-11-20T10:45:25Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"fea689e037f302e54a774513ded0ddd8f674bcf18fc94acf02977ce815cc215a","abstract_canon_sha256":"2077d26e37b446c447b04cad372ae23507c7cd6b5addc159c9dbf2c27e78241b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:13.978980Z","signature_b64":"DHtYwBesrnm/xbwvs8x/+i6+sgQLMo/AkUT4fiOP3zsoS6t8zevWIcmU8qVS5QSuedoqnGgOrsG0t/LysPo5Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e7036095c9815278f018ca3a680cffdd0fe91ac7e5f3852ba83d81af1508b14","last_reissued_at":"2026-05-18T00:00:13.978543Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:13.978543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the structure of abelian profinite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GR","authors_text":"Mar\\'ia V. Ferrer, Salvador Hern\\'andez","submitted_at":"2018-11-20T10:45:25Z","abstract_excerpt":"A subgroup $G$ of a product $\\prod\\limits_{i\\in\\mathbb{N}}G_i$ is \\emph{rectangular} if there are subgroups $H_i$ of $G_i$ such that $G=\\prod\\limits_{i\\in\\mathbb{N}}H_i$. We say that $G$ is \\emph{weakly rectangular} if there are finite subsets $F_i\\subseteq \\mathbb{N}$ and subgroups $H_i$ of $\\bigoplus\\limits_{j\\in F_i} G_j$ that satisfy $G=\\prod\\limits_{i\\in\\mathbb{N}}H_i$. %We say that $G$ is a \\emph{subdirect product} of the family $\\{G_i\\}_{i\\in I}$ if $G$ is weakly rectangular and %$G\\cap\\bigoplus\\limits_{i\\in I} G_i=\\bigoplus\\limits_{i\\in\\mathbb{N}}H_i$. 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