International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1981 / Article

Open Access

Volume 4 |Article ID 787626 | https://doi.org/10.1155/S0161171281000549

T. G. Ostrom, "Collineation groups of translation planes of small dimension", International Journal of Mathematics and Mathematical Sciences, vol. 4, Article ID 787626, 14 pages, 1981. https://doi.org/10.1155/S0161171281000549

Collineation groups of translation planes of small dimension

Received03 Sep 1980
Revised30 Mar 1981

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 w2a+b where wa 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.

Copyright © 1981 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


More related articles

 PDF Download Citation Citation
 Order printed copiesOrder
Views77
Downloads350
Citations

We are committed to sharing findings related to COVID-19 as quickly as possible. We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. Review articles are excluded from this waiver policy. Sign up here as a reviewer to help fast-track new submissions.