Action of PGL(2,q) on the Cosets of the Centralizer of an Eliptic Element
Kimani, Patrick Mwangi
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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 PGL(2,q) centralizer of an elliptic element which is a non maximal subgroup c(q+1). 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 [q+ 1][q-2].