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Schreier type theorems for bicrossed products

Central European Journal of Mathematics

Abstract

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: GH 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 GH α′⋈β′ (G, *). Moreover, if we fix the group H and the automorphism σ ∈ Aut H then any σ-invariant isomorphism H α⋈β GH 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.

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Correspondence to Ana Agore.

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Agore, A., Militaru, G. Schreier type theorems for bicrossed products. centr.eur.j.math. 10, 722–739 (2012). https://doi.org/10.2478/s11533-011-0128-6

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  • DOI: https://doi.org/10.2478/s11533-011-0128-6

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