Action of PGL(2,q) on the Cosets of the Centralizer of an Eliptic Element
Patrick Mwangi Kimani *
Department of Mathematics, Computing and I.T, University of Kabianga, Embu, Kenya.
Daniel Adicka
Department of Mathematics and Computer Science, University of Kabianga, P. O. Box 2030-20200, Kericho, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Most researchers consider the action of projective general group on the cosets of its maximal subgroups leaving out non-maximal subgroups. In this paper, we consider the action of 
centralizer of an elliptic element which is a non maximal subgroup 
. In particular, we determine the subdegrees, rank and properties of the suborbital graphs of the action. We achieve this through the application of the action of a group by conjugation. We have proved that the rank is q and the subdegrees are 
and 
.
Keywords: Rank, subdegrees, centralizer, suborbital graphs