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This result applies to fractal nonabelian groups with torsion-free abelianization, for example the Basilica group, the Brunner-Sidki-Vieira group, and also to the GGS-group with constant defining vector.\n  We further provide two examples showing that neither of the requirements $|G':\\mathrm{st}_G(1)'|=\\infty$ and being fractal can be dropped."},"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":"1801.04595","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-01-14T18:51:54Z","cross_cats_sorted":[],"title_canon_sha256":"5a2d6ce6c168994e598de845f59e1f6d1dbed71ad919fdd6792323351724a5c2","abstract_canon_sha256":"0b084568692742dedff3bebdd64b76984cb9bbe24007fc5ab05a9e954b429d34"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:41.217959Z","signature_b64":"9BU5dfVDLCB0L8blr3lGOvIE/lgpUgEI9KgKrkuNuqRYCZ9sB7BVt9R/vVEnAgpzd3777vAIoCW1agCBY7y+Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a349772ffca14318159a6a5734a045103ccbe1c554a4701299bce21c3d8ca267","last_reissued_at":"2026-05-18T00:19:41.217323Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:41.217323Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Engel elements in some fractal groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Albert Garreta, Gustavo A. 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