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A subgroup $H$ of an abstract residually ${\\cal C}$ group $R$ is said to be conjugacy ${\\cal C}$-distinguished if whenever $y\\in R$, then $y$ has a conjugate in $H$ if and only if the same holds for the images of $y$ and $H$ in every quotient group $R/N\\in {\\cal C}$ of $R$. We prove that in a group having a normal free subgroup $\\Phi$ such that $R/\\Phi$ is in ${\\cal C}$, every finitely generated subgroup is conjugacy ${\\cal C}$-distinguished. We also prove that finitely generat"},"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":"1504.02982","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-04-12T15:22:22Z","cross_cats_sorted":[],"title_canon_sha256":"cc4fa00c9e615bcdcda001544818207dd11f230ec425443d1ba51294d9c530db","abstract_canon_sha256":"7bb32e2f6866010c442fe325d1e34530c9e7fac1a8d90b07af0e8723c9020205"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:10.426704Z","signature_b64":"mp9V+HwE805+Fr/9QJtOYol1UW5LPDrUI1LPIEkOiSwi6BgvfYE90SfgxJROMI7KIA1yvif2KVq6pEkW3hctCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69d84d3bf69b55b602db2d8d0d1178c2dac1cd6eac465f6d994d2b8644fec496","last_reissued_at":"2026-05-18T01:32:10.426056Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:10.426056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conjugacy Distinguished Subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Luis Ribes, Pavel Zalesskii","submitted_at":"2015-04-12T15:22:22Z","abstract_excerpt":"Let ${\\cal C}$ be a nonempty class of finite groups closed under taking subgroups, homomorphic images and extensions. 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