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; α; β) is deformed using a combinatorial datum (σ; v; r) consisting of an automorphism σ of H, a permutation v of the set G and a transition map r: G → H in order to obtain a new matched pair (H; (G; *); α′, β′) such that there exists a σ-invariant isomorphism of groups H α⋈β G ≅H α′⋈β′ (G, *). Moreover, if we fix the group H and the automorphism σ ∈ Aut H then any σ-invariant isomorphism H α⋈β G ≅ H α′⋈β′ G′ between two arbitrary bicrossed product of groups is obtained in a unique way by the above deformation method. As applications two Schreier type classification theorems for bicrossed products of groups are given.
@article{bwmeta1.element.doi-10_2478_s11533-011-0128-6,
author = {Ana Agore and Gigel Militaru},
title = {Schreier type theorems for bicrossed products},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {722-739},
zbl = {1271.20038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0128-6}
}
Ana Agore; Gigel Militaru. Schreier type theorems for bicrossed products. Open Mathematics, Tome 10 (2012) pp. 722-739. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0128-6/
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