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Collineation group as a subgroup of the symmetric group

Fedor Bogomolov, Marat Rovinsky (2013)

Open Mathematics

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 𝔖 ψ 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.,...

Highly transitive subgroups of the symmetric group on the natural numbers

U. B. Darji, J. D. Mitchell (2008)

Colloquium Mathematicae

Highly transitive subgroups of the symmetric group on the natural numbers are studied using combinatorics and the Baire category method. In particular, elementary combinatorial arguments are used to prove that given any nonidentity permutation α on ℕ there is another permutation β on ℕ such that the subgroup generated by α and β is highly transitive. The Baire category method is used to prove that for certain types of permutation α there are many such possibilities for β. As a simple corollary,...

The Farey graph.

Jones, Gareth A. (1987)

Séminaire Lotharingien de Combinatoire [electronic only]

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