Collineation groups of translation planes of small dimension

T. G. Ostrom

International Journal of Mathematics and Mathematical Sciences, 1981, vol. 4, 1-14

Abstract:

A subgroup of the linear translation complement of a translation plane is geometrically irreducible if it has no invariant lines or subplanes. A similar definition can be given for geometrically primitive. If a group is geometrically primitive and solvable then it is fixed point free or metacyclic or has a normal subgroup of order w 2 a + b where w a divides the dimension of the vector space. Similar conditions hold for solvable normal subgroups of geometrically primitive nonsolvable groups. When the dimension of the vector space is small there are restrictions on the group which might possibly be in the translation complement. We look at the situation for certain orders of the plane.

Date: 1981
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/4/787626.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/4/787626.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:787626

DOI: 10.1155/S0161171281000549

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().