Block transitive automorphism groups of designs
type: Item
instance of: scholarly article
title: Block transitive automorphism groups of designs
zbMATH Open document ID: 0542.05013
DOI: 10.1016/0021-8693(84)90047-4
author: Terence M. Gagen
author: A. R. Camina
published in: Journal of Algebra
publication date: 1984-01-01T00:00:00Z
review text: The authors prove the following result: Let G be a block-transitive group of automorphisms of a 2-(v,k,l)design, where k divides v. Then (i) G is transitive on flags and (ii) G/S(G) has a simple socle. (Note: flag is an incident point pair and S(G) denotes the maximal soluble normal subgroup of G.) The proof of (i) is straightforward. Then (i) implies that G is primitive on points. The use of the O'Nan and Scott theorem together with some results of \textit{C. Hering} [Geom. Dedicata 2, 425-460 (1974; Zbl 0292.20045)] then enables (ii) to be proved.
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 3861173
zbMATH Keywords: block-transitive group
zbMATH Keywords: 2-design
reviewed by: Ascher Wagner
MaRDI profile type: Publication
full work available at URL: 0021-8693(84)90047-4
OpenAlex ID: W2027912074
cites work: Finite Permutation Groups and Finite Simple Groups
cites work: Q5545191
cites work: Transitive linear groups and linear groups which contain irreducible subgroups of prime order
cites work: On finite affine line transitive planes
description: scientific article; zbMATH DE number 3861173