Subgroups and Orbits by Companion Matrix in Three Dimensional Projective Space

Abstract

The aim of this paper is to construct cyclic subgroups of the projective general linear group over from the companion matrix, and then form caps of various degrees in . Geometric properties of these caps as secant distributions and index distributions are given and determined if they are complete. Also, partitioned of into disjoint lines is discussed.

Keywords

• Cap, Companion matrix, Group action, Projective geometry, Secant