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Line‐Transitive Automorphism Groups of Linear Spaces

Line‐Transitive Automorphism Groups of Linear Spaces LINE-TRANSITIVE AUTOMORPHISM GROUPS OF LINEAR SPACES ALAN R. CAMINA AND CHERYL E. PRAEGER 1. Introduction A linear space Sfisa. set & of points, together with a set i f of distinguished subsets called lines, such that any two points lie on exactly one line. In this paper we shall be concerned with linear spaces in which every line has the same number of points, and we shall call such a system a regular linear space. Moreover, we shall also assume that & is finite and that \S£\ < oo. In the literature, a finite regular linear space is also called a 2-(v,k, 1) block design, where v = \^\, but the motivation for our work came from results in [3,11] (about linear spaces), and so we shall use the language of linear spaces. The number of points will be denoted by v and the number of lines by b. We shall also denote the number of points on a line by k and the number of lines through a point by r. We shall assume that k > 2. In this paper we investigate the normal subgroup structure of an automorphism group of a finite linear space which is http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Line‐Transitive Automorphism Groups of Linear Spaces

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Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/25.4.309
Publisher site
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Abstract

LINE-TRANSITIVE AUTOMORPHISM GROUPS OF LINEAR SPACES ALAN R. CAMINA AND CHERYL E. PRAEGER 1. Introduction A linear space Sfisa. set & of points, together with a set i f of distinguished subsets called lines, such that any two points lie on exactly one line. In this paper we shall be concerned with linear spaces in which every line has the same number of points, and we shall call such a system a regular linear space. Moreover, we shall also assume that & is finite and that \S£\ < oo. In the literature, a finite regular linear space is also called a 2-(v,k, 1) block design, where v = \^\, but the motivation for our work came from results in [3,11] (about linear spaces), and so we shall use the language of linear spaces. The number of points will be denoted by v and the number of lines by b. We shall also denote the number of points on a line by k and the number of lines through a point by r. We shall assume that k > 2. In this paper we investigate the normal subgroup structure of an automorphism group of a finite linear space which is

Journal

Bulletin of the London Mathematical Society – Wiley

Published: Jul 1, 1993

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