Biplanes with flag-transitive automorphism groups of almost simple type, with exceptional socle of Lie type.
type: Item
instance of: scholarly article
title: Biplanes with flag-transitive automorphism groups of almost simple type, with exceptional socle of Lie type.
zbMATH Open document ID: 1172.20001
author: Eugenia O'Reilly-Regueiro
published in: Journal of Algebraic Combinatorics
publication date: 2008-06-30T00:00:00Z
review text: This paper completes the classification of symmetric \(2\)-\((v,k,2)\) designs, these are sometimes called biplanes, which have flag-transitive almost simple automorphism groups. The author, in a sequence of papers based on her Ph.D thesis [J. Comb. Theory, Ser. A 109, No. 1, 135-148 (2005; Zbl 1055.05014); Eur. J. Comb. 26, No. 5, 577-584 (2005; Zbl 1113.20003); J. Algebr. Comb. 26, No. 4, 529-552 (2007; Zbl 1126.05023)], has considered the other cases. The paper depends on some very detailed and specific information about the structure of maximal subgroups of the exceptional groups of Lie type. The combination of all these papers is that if \(D\) is a biplane with a primitive, flag-transitive automorphism group of almost simple type then \(D\) has parameters either \((7,4,2)\) or \((11,5,2)\) and is unique up to isomorphism.
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 20D06
zbMATH DE Number: 5294576
zbMATH Keywords: flag-transitive automorphism groups
zbMATH Keywords: primitive groups
zbMATH Keywords: symmetric block designs
zbMATH Keywords: biplanes
zbMATH Keywords: exceptional groups of Lie type
Wikidata QID: Q115383756
reviewed by: A. R. Camina
MaRDI profile type: Publication
full work available at URL: s10801-007-0098-8
OpenAlex ID: W2006551784
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DOI: 10.1007/S10801-007-0098-8
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description: scientific article; zbMATH DE number 5294576