Collineation group as a subgroup of the symmetric group

• Autorzy: Fedor Bogomolov , Marat Rovinsky
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

Projective group; Collineations; Symmetric groups

Kategorie tematyczne

• 20B35: Subgroups of symmetric groups
• 20B22: Multiply transitive infinite groups

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 1
• Strony: 17-26

Daty

wydano

2013-01-01

online

2012-10-24

Twórcy

autor

Fedor Bogomolov

autor

Marat Rovinsky

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0131-6