Biplanes (56,11,2) with automorphisms of order 4 fixing some point
type: Item
instance of: scholarly article
title: Biplanes (56,11,2) with automorphisms of order 4 fixing some point
zbMATH Open document ID: 0662.05009
DOI: 10.1016/0012-365X(88)90026-X
published in: Discrete Mathematics
publication date: 1988-01-01T00:00:00Z
review text: The authors show that all biplanes of order 9 (i.e., all symmetric designs \(S_ 2(2,11,56))\) which admit an automorphism of order 4 fixing one point are known. One obtains the 4 examples which have been known for some time [cf. e.g. \textit{C. J. Salwach} and \textit{J. A. Mezzaroba}: ``The four known biplanes with \(k=11\), Intern. J. Math. Math. Sci. 2, 251-260 (1979; Zbl 0411.51006)]. (There is a fifth biplane recently obtained by \textit{Z. Janko} and \textit{T. van Trung} [``A new biplane of order 9 with a small automorphism group'', J. Comb. Theory, Ser. A 42, 305-309 (1986)] but it does not admit such an automorphism of order 4.) The proof uses standard arguments and a computer.
reviewed by: Dieter Jungnickel
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 4081569
zbMATH Keywords: symmetric design
zbMATH Keywords: biplanes
author: Vladimir Ćepulić
author: Mario Essert
MaRDI profile type: Publication
cites work: On collineation groups of symmetric block designs
cites work: Q5202667
cites work: Q4723752
cites work: Q5184922
cites work: A new biplane of order 9 with a small automorphism group
cites work: Q3762332
cites work: The four known biplanes with k=11
Wikidata QID: Q126400511
description: scientific article; zbMATH DE number 4081569