Displaying similar documents to “Remarks on duality for Σ -groups. I. Products and coproducts”

On the structure of the augmentation quotient group for some nonabelian 2-groups

Jizhu Nan, Huifang Zhao (2012)

Czechoslovak Mathematical Journal

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Let G be a finite nonabelian group, ℤ G its associated integral group ring, and ▵ ( G ) its augmentation ideal. For the semidihedral group and another nonabelian 2-group the problem of their augmentation ideals and quotient groups Q n ( G ) = ▵ n ( G ) / ▵ n + 1 ( G ) is deal with. An explicit basis for the augmentation ideal is obtained, so that the structure of its quotient groups can be determined.

Schreier type theorems for bicrossed products

Ana Agore, Gigel Militaru (2012)

Open Mathematics

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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...