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 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 of . We show in Theorem 3.1 that H = , if ψ is infinite.
@article{bwmeta1.element.doi-10_2478_s11533-012-0131-6,
author = {Fedor Bogomolov and Marat Rovinsky},
title = {Collineation group as a subgroup of the symmetric group},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {17-26},
zbl = {1277.20003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0131-6}
}
Fedor Bogomolov; Marat Rovinsky. Collineation group as a subgroup of the symmetric group. Open Mathematics, Tome 11 (2013) pp. 17-26. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0131-6/
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