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Recognizability of finite groups by Suzuki group

Alireza Khalili Asboei, Seyed Sadegh Salehi Amiri (2019)

Archivum Mathematicum

Let G be a finite group. The main supergraph 𝒮 ( G ) is a graph with vertex set G in which two vertices x and y are adjacent if and only if o ( x ) o ( y ) or o ( y ) o ( x ) . In this paper, we will show that G S z ( q ) if and only if 𝒮 ( G ) 𝒮 ( S z ( q ) ) , where q = 2 2 m + 1 8 .

Schreier type theorems for bicrossed products

Ana Agore, Gigel Militaru (2012)

Open Mathematics

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...

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