\(m\)th-root subgeometry partitions
type: Item
instance of: scholarly article
title: \(m\)th-root subgeometry partitions
zbMATH Open document ID: 1190.51007
author: Norman L. Johnson
published in: Designs, Codes and Cryptography
publication date: 2009-03-31T00:00:00Z
review text: It is shown that for suitable conditions on \(m\), \(n\) and \(q\), two construction methods for flag-transitive designs due to \textit{W. M. Kantor} [in: Jungnickel D., Vanstone S.A., Arasu K.T., Aschbacher M., Foote R. (eds.). Proceedings of Marshall Hall Conference (Burlington, VT, 1990), Wiley, New York 13--30 (1993)] give rise to partitions of finite projective spaces \(PG(n-1, q^m)\) into subgeometries isomorphic to \(PG(n-1, q)\) such that these subgeometries form an orbit of a cyclic collineation group. Moreover, if \(l\) divides \(m\), then every partition of \(PG(n-1, q^m)\) into subgeometries isomorphic to \(PG(n-1, q)\) gives rise to such a partition of \(PG(mn/l -1, q^l)\).
reviewed by: Theo Grundhöfer
Mathematics Subject Classification ID: 51E23
Mathematics Subject Classification ID: 51A40
zbMATH DE Number: 5536699
zbMATH Keywords: finite projective space
zbMATH Keywords: partition
zbMATH Keywords: subgeometry
MaRDI profile type: Publication
full work available at URL: s10623-007-9141-y
OpenAlex ID: W2079901855
cites work: Baer subgeometry partitions
cites work: Perfect Baer subplane partition and three-dimensional flag-transitive planes
cites work: Mixed partitions and related designs
cites work: Q4003762
cites work: Retracting spreads
cites work: Quasi-subgeometry partitions of projective spaces
cites work: Constructions of subgeometry partitions
DOI: 10.1007/S10623-007-9141-Y
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description: scientific article; zbMATH DE number 5536699