{"paper":{"title":"Schreier type theorems for bicrossed products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"A.L. Agore, G. Militaru","submitted_at":"2009-03-29T16:05:28Z","abstract_excerpt":"We prove that the bicrossed product of two groups is a quotient of the pushout of two semidirect products. A matched pair of groups $(H, G, \\alpha, \\beta)$ is deformed using a combinatorial datum $(\\sigma, v, r)$ consisting of an automorphism $\\sigma$ of $H$, a permutation $v$ of the set $G$ and a transition map $r: G\\to H$ in order to obtain a new matched pair $\\bigl(H, (G,*), \\alpha', \\beta' \\bigl)$ such that there exist an $\\sigma$-invariant isomorphism of groups $H {}_{\\alpha} \\bowtie_{\\beta} G \\cong H {}_{\\alpha'} \\bowtie_{\\beta'} (G,*)$. Moreover, if we fix the group $H$ and the automorp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.5060","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}