Browsing by Author "Adicka, Daniel"

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    Action of PGL(2,q) on the Cosets of the Centralizer of an Eliptic Element
    (Uoem, 2021-08-19) Kimani, Patrick Mwangi; Adicka, Daniel
    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].
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    Action ofPGL (2 ,q ) on the Cosets of the Centralizer of an Eliptic Element
    (UoEm, 2021) Kimani, patrick; Adicka, Daniel
    Most researchers consider the action of projective general group on the cosets of its maximal subgroups leaving out non-maximal subgroupsCq+1. In this paper, we consider the action ofPGL (2, ) 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 and the subdegrees are [1][ ] and [ + 1][ ] .