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The question is asked of an upper bound on the solvability length of finite $2$-groups generated by involutions in which every involution (not only the generators) is also left $2$-Engel. We negatively answer the question."},"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":"1404.4558","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-04-17T15:33:31Z","cross_cats_sorted":[],"title_canon_sha256":"e7f8fa4398722f726d8adb407677fc4ae32548571c92c1e4f7fc10ae69a02db6","abstract_canon_sha256":"a012721d3967c44977b3f8a6e690550e4d002aebeda437302ff8c3a701063204"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:59.312019Z","signature_b64":"4N3NChX1MWVZ00BOy/F5Rk9NHmC/DH7cVQLQJTH1sE7lwH4TEO6FyBAqWc7xGB/8F3kWtLBcVjf9KIyekNDTBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2447a3808602bbb3d8bc83bc2777932df5511b67f45c0a794d031e30e2b38ef","last_reissued_at":"2026-05-18T00:56:59.311644Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:59.311644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-solvable groups generated by involutions in which every involution is left $2$-Engel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alireza Abdollahi","submitted_at":"2014-04-17T15:33:31Z","abstract_excerpt":"The following problem is proposed as Problem 18.57 in [The Kourovka Notebook, No. 18, 2014] by D. 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