The automorphism groups of doubly transitive bilinear dual hyperovals
type: Item
instance of: scholarly article
title: The automorphism groups of doubly transitive bilinear dual hyperovals
zbMATH Open document ID: 1441.20002
author: Ulrich Dempwolff
publication date: 2018-03-29T00:00:00Z
review text: A dual hyperoval over the field \({\mathbb F}_2\) of rank \(n\) is a set \(D\) of \(2^n-1\) subspaces of some vector space \({\mathbb F}_2^m\) such that \(\dim(X\cap Y) =1\) and \(\dim(X\cap Y\cap Z) =0\) for any three distinct elements \(X,Y, Z \in D\). The author shows that the examples constructed by him in [Eur. J. Comb. 44, Part A, 1--22 (2015; Zbl 1341.51008)], Example 3.3, have the automorphism group \(\mathrm{A\Gamma L}(1,2^n)\). Moreover, he characterizes the \(2\)-transitive quotients of the examples of \textit{C. Huybrechts} [Discrete Math. 255, No. 1--3, 193--223 (2002; Zbl 1024.51010)] and determines their automorphism groups; the number of such quotients grows exponentially with \(n\).
reviewed by: Theo Grundhöfer
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 51E21
zbMATH DE Number: 6854787
zbMATH Keywords: dual hyperoval
zbMATH Keywords: automorphism group
describes a project that uses: GAP
MaRDI profile type: Publication
full work available at URL: advgeom-2016-0030
OpenAlex ID: W2588590598
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DOI: 10.1515/ADVGEOM-2016-0030
published in: advg
description: scientific article; zbMATH DE number 6854787