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1
Content available remote

Collineation group as a subgroup of the symmetric group

100%
Bogomolov F., Rovinsky M.
Open Mathematics
|
2013
|
tom 11
|
nr 1
17-26
EN
Let ψ be the projectivization (i.e., the set of one-dimensional vector subspaces) of a vector space of dimension ≥ 3 over a field. Let H be a closed (in the pointwise convergence topology) subgroup of the permutation group $\mathfrak{S}_\psi $ of the set ψ. Suppose that H contains the projective group and an arbitrary self-bijection of ψ transforming a triple of collinear points to a non-collinear triple. It is well known from [Kantor W.M., McDonough T.P., On the maximality of PSL(d+1,q), d ≥ 2, J. London Math. Soc., 1974, 8(3), 426] that if ψ is finite then H contains the alternating subgroup $\mathfrak{A}_\psi $ of $\mathfrak{S}_\psi $. We show in Theorem 3.1 that H = $\mathfrak{S}_\psi $, if ψ is infinite.
2
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Schreier type theorems for bicrossed products

64%
Agore A., Militaru G.
Open Mathematics
|
2012
|
tom 10
|
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.
3
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Unramified cohomology of alternating groups

64%
Bogomolov F., Petrov T.
Open Mathematics
|
2011
|
tom 9
|
nr 5
936-948
EN
We prove vanishing results for the unramified stable cohomology of alternating groups.
4
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Perfectly supportable semigroups are σ-discrete in each Hausdorff shift-invariant topology

64%
Banakh T., Guran I.
Topological Algebra and its Applications
|
2013
|
tom 1
1-8
EN
In this paper we introduce perfectly supportable semigroups and prove that they are σ-discrete in each Hausdorff shiftinvariant topology. The class of perfectly supportable semigroups includes each semigroup S such that FSym(X) ⊂ S ⊂ FRel(X) where FRel(X) is the semigroup of finitely supported relations on an infinite set X and FSym(X) is the group of finitely supported permutations of X.
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