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Schreier type theorems for bicrossed products

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Agore A., Militaru G.

Open Mathematics

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2012

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tom 10

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nr 2

722-739

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.

2

Solitary quotients of finite groups

100%

Tărnăuceanu M.

Open Mathematics

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2012

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tom 10

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nr 2

740-747

EN

We introduce and study the lattice of normal subgroups of a group G that determine solitary quotients. It is closely connected to the well-known lattice of solitary subgroups of G, see [Kaplan G., Levy D., Solitary subgroups, Comm. Algebra, 2009, 37(6), 1873–1883]. A precise description of this lattice is given for some particular classes of finite groups.

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Erratum to: “Solitary quotients of finite groups”

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Tărnăuceanu M.

Open Mathematics

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2013

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tom 11

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nr 2

376-377

EN

In this short note a correct proof of Theorem 3.3 from [Tărnăuceanu M., Solitary quotients of finite groups, Cent. Eur. J. Math., 2012, 10(2), 740–747] is given.

Ograniczanie wyników

3 Open Mathematics

2 Tărnăuceanu M.

1 Agore A.

1 Militaru G.

1 2013

2 2012

Schreier type theorems for bicrossed products

Solitary quotients of finite groups

Erratum to: “Solitary quotients of finite groups”