A characterization of finite symplectic polar spaces of odd prime order
type: Item
instance of: scholarly article
title: A characterization of finite symplectic polar spaces of odd prime order
zbMATH Open document ID: 1115.51001
author: Binod K. Sahoo
author: N. S. Narasimha Sastry
published in: Journal of Combinatorial Theory. Series A
publication date: 2006-12-14T00:00:00Z
review text: Let \(p\) be a prime and let \(S = (P,L)\) be a partial linear space such that each line of \(S\) contains \(p+1\) points. A representation of \(S\) consisists of a group \(R\) and a mapping \(\psi\) from \(P\) to the set of subgroups of order \(p\) of \(R\) such that \(R\) is generated by the subgroups \(\psi(x)\), \(x \in P\), and for each line \(l \in L\) the subgroups \(\psi(x)\), \(x \in l\), are distinct and generate an elementary abelian subgroup of order \(p^ 2\). The authors show that if \(S\) is a finite polar space of rank \(r \geq 2\) and \(R\) is nonabelian, then \(p\) is odd, \(S\) is isomorphic to the symplectic polar space \(W_{2r}(p)\), and \(R\) is an extraspecial \(p\)-group of order \(p^{1+2r}\) and exponent \(p\). Moreover, the representation is unique.
reviewed by: Norbert Knarr
Mathematics Subject Classification ID: 51A50
zbMATH DE Number: 5080377
zbMATH Keywords: generalized quadrangles
zbMATH Keywords: polar spaces
zbMATH Keywords: nonabelian representations
zbMATH Keywords: extraspecial \(p\)-groups
MaRDI profile type: Publication
full work available at URL: j.jcta.2006.03.001
OpenAlex ID: W2152174022
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DOI: 10.1016/J.JCTA.2006.03.001
description: scientific article; zbMATH DE number 5080377