On multiplier groups of finite cyclic planes
type: Item
instance of: scholarly article
title: On multiplier groups of finite cyclic planes
zbMATH Open document ID: 0673.51007
DOI: 10.1016/0021-8693(89)90249-4
published in: Journal of Algebra
publication date: 1989-01-01T00:00:00Z
review text: Let \(S\) be a cyclic group of collineations acting (sharply) transitively on the points of a finite projective plane of order \(n\); then \(S\) is called a Singer group. The multiplier group is the quotient \(M=N/S\), where \(N\) is the normalizer of \(S\) in the collineation group. The author proves the following results: The Sylow 2-subgroup of \(M\) is cyclic. If \(| M| =3k\) with \(k\in \{3,5,2^a|\) \(a\in\mathbb{N}_0\}\), then \(n=p^k\) for some prime \(p\). If \(| \Aut(S):M| \in \{2,4\}\), then \(n\leq 4\).
reviewed by: Theo Grundhöfer
Mathematics Subject Classification ID: 51E15
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 05B10
zbMATH DE Number: 4101977
zbMATH Keywords: finite projective plane
zbMATH Keywords: Singer group
zbMATH Keywords: multiplier
author: Chat-Yin Ho
MaRDI profile type: Publication
full work available at URL: 0021-8693(89)90249-4
OpenAlex ID: W2001377866
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description: scientific article; zbMATH DE number 4101977