Steiner triple systems with a doubly transitive automorphism group
type: Item
instance of: scholarly article
title: Steiner triple systems with a doubly transitive automorphism group
zbMATH Open document ID: 0579.05017
DOI: 10.1016/0097-3165(85)90069-X
author: Marshall jun. Hall
published in: Journal of Combinatorial Theory. Series A
publication date: 1985-01-01T00:00:00Z
review text: This paper proves that a Steiner triple system with a doubly transitive automorphism group is either an affine space over GF(3) or a projective space over GF(2). This settles the author's conjecture made in 1960 in the affirmative. The proof is in two cases, the first case is due to J. T. Hall in his M.Sc Thesis, and the second case depends on the classification of the finite simple groups. The exposition is clear and the reader with some background in group theory will appreciate its beauty.
Mathematics Subject Classification ID: 05B07
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 51E10
zbMATH DE Number: 3926935
zbMATH Keywords: affine space
zbMATH Keywords: Steiner triple system
zbMATH Keywords: automorphism group
zbMATH Keywords: projective space
MaRDI profile type: Publication
cites work: Finite Permutation Groups and Finite Simple Groups
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cites work: STEINER TRIPLE SYSTEMS WITH GEOMETRIC MINIMALLY GENERATED SUBSYSTEMS
cites work: Q5721210
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description: scientific article; zbMATH DE number 3926935