Action of PGL(2,q) on the Cosets of the Centralizer of an Eliptic Element - Kimani, Patrick Mwangi; Adicka, Daniel (Uoem, 2021)
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 [1][2] and [q+ 1][q-2].
Keywords: Rank; subdegrees; centralizer; suborbital graphs.