Schreier type theorems for bicrossed products

• Autorzy: Ana Agore , Gigel Militaru
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Matched pairs; Bicrossed product of groups

Kategorie tematyczne

• 20B05: General theory for finite groups
• 20D06: Simple groups: alternating groups and groups of Lie type
• 20B35: Subgroups of symmetric groups
• 20D40: Products of subgroups

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 2
• Strony: 722-739

Daty

wydano

2012-04-01

online

2012-01-18

Twórcy

autor

Ana Agore

• Vrije Universiteit Brussel

autor

Gigel Militaru

• University of Bucharest

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-011-0128-6