Stabilizers of collineation groups of smooth stable planes

Bödi, Richard

doi:10.1016/S0019-3577(98)80028-1

Publication type:	Article in scientific journal
Type of review:	Peer review (publication)
Title:	Stabilizers of collineation groups of smooth stable planes
Authors:	Bödi, Richard
DOI:	10.1016/S0019-3577(98)80028-1
Published in:	Indagationes Mathematicae
Volume(Issue):	9
Issue:	4
Page(s):	477
Pages to:	490
Issue Date:	1998
Publisher / Ed. Institution:	Elsevier
Publisher / Ed. Institution:	Amsterdam
ISSN:	0019-3577
Language:	English
Subject (DDC):	510: Mathematics
Abstract:	Let S be a smooth stable plane of dimension n (see Definition 1.2) and let Δ be a closed subgroup of the collineation group of S which fixes some point p. We derive some results on the group-theoretical structure of Δ, e.g. that Δ is a linear Lie group (Theorem 3.7). As a by-product this shows that no (affine or projective) Moulton plane can be turned into a smooth plane. If Δ fixes some flag, then any Levi subgroup Ψ of Δ is a compact group and Δ is contained in the flag stabilizer of the classical Moufang plane of dimension n (Corollary 3.1 and Theorem 3.7). Let Δ fix three concurrent lines through the point p. If is one of the classical projective planes over the reals, the complex numbers, the quaternions, or the Cayley numbers, then the dimension of Δ is dclass = 3, 6, 15, or 38, respectively. We show that for a smooth stable (projective) plane S of dimension 2l either S is an almost projective translation plane (classical projective plane) or that dim Δ ≤ dclass − l holds (Theorems 4.1 and 4.2).
URI:	https://digitalcollection.zhaw.ch/handle/11475/3225
Fulltext version:	Published version
License (according to publishing contract):	Licence according to publishing contract
Departement:	School of Engineering
Appears in collections:	Publikationen School of Engineering

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Bödi, R. (1998). Stabilizers of collineation groups of smooth stable planes. Indagationes Mathematicae, 9(4), 477–490. https://doi.org/10.1016/S0019-3577(98)80028-1

Bödi, R. (1998) ‘Stabilizers of collineation groups of smooth stable planes’, Indagationes Mathematicae, 9(4), pp. 477–490. Available at: https://doi.org/10.1016/S0019-3577(98)80028-1.

R. Bödi, “Stabilizers of collineation groups of smooth stable planes,” Indagationes Mathematicae, vol. 9, no. 4, pp. 477–490, 1998, doi: 10.1016/S0019-3577(98)80028-1.

BÖDI, Richard, 1998. Stabilizers of collineation groups of smooth stable planes. Indagationes Mathematicae. 1998. Bd. 9, Nr. 4, S. 477–490. DOI 10.1016/S0019-3577(98)80028-1

Bödi, Richard. 1998. “Stabilizers of Collineation Groups of Smooth Stable Planes.” Indagationes Mathematicae 9 (4): 477–90. https://doi.org/10.1016/S0019-3577(98)80028-1.

Bödi, Richard. “Stabilizers of Collineation Groups of Smooth Stable Planes.” Indagationes Mathematicae, vol. 9, no. 4, 1998, pp. 477–90, https://doi.org/10.1016/S0019-3577(98)80028-1.