A new class of translation planes constructed by hyper-regulus replacement
type: Item
instance of: scholarly article
title: A new class of translation planes constructed by hyper-regulus replacement
zbMATH Open document ID: 1176.51005
author: Vikram Jha
author: Norman L. Johnson
published in: Journal of Geometry
publication date: 2009-06-08T00:00:00Z
review text: A class of hyper-reguli is determined in a Desarguesian affine plane that are not André hyper-reguli. It is considered the class of translation planes obtained by the replacement of such a hyper-regulus and shown that it is obtained a new class of translation planes, which are not André or generalized André. These planes have a very small affine homology group, whereas in the André or generalized André planes the affine homology group is rather larger. In fact, when \(n\) and \(q\) are both greater then 3, and \(n\) is odd, the affine homology group of these planes is trivial.
reviewed by: Milica Stojanović
Mathematics Subject Classification ID: 51E23
Mathematics Subject Classification ID: 51A40
zbMATH DE Number: 5562605
zbMATH Keywords: hyper-regulus
zbMATH Keywords: multiple replacement
zbMATH Keywords: André hyper-reguli
MaRDI profile type: Publication
full work available at URL: s00022-008-1976-5
OpenAlex ID: W1966394414
DOI: 10.1007/S00022-008-1976-5
description: scientific article; zbMATH DE number 5562605