Journal of Applied Mathematics
Volume 2012 (2012), Article ID 387132, 16 pages
Research Article

Lattices Generated by Orbits of Subspaces under Finite Singular Orthogonal Groups II

College of Science, Civil Aviation University of China, Tianjin 300300, China

Received 28 March 2012; Accepted 15 June 2012

Academic Editor: Ch Tsitouras

Copyright © 2012 You Gao and XinZhi Fu. 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.


Let be a -dimensional vector space over the finite field . In this paper we assume that is a finite field of odd characteristic, and the singular orthogonal groups of degree over . Let be any orbit of subspaces under . Denote by the set of subspaces which are intersections of subspaces in , where we make the convention that the intersection of an empty set of subspaces of is assumed to be . By ordering by ordinary or reverse inclusion, two lattices are obtained. This paper studies the questions when these lattices are geometric lattices.