Browsing by Author "Kimani, Patrick Mwangi"

Now showing 1 - 5 of 5
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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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    Cycle Index Formulas for D n Acting on Unordered Pairs
    (Uoem, 2015) Muthoka, Geoffrey; Kamuti, Ireri; Lao, Hussein; Kimani, Patrick Mwangi
    The cycle index of dihedral group D n acting on the set of X the vertices of a regular n- gon was studied (See [1]). In this paper we study the cycle index formulas of D n acting on unordered pairs from the set . In each case the actions of the cyclic part and the reflection part are studied separately for both an even value of and an odd value of .1.
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    Kimani, Patrick Mwangi
    (UoEm, 2023) Kimani, Patrick Mwangi
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    Rank and Subdegrees of PGL(2; q) Acting Cosets of PGL(2; e) for q an Even Power of e
    (UoEm, 2019) Kimani, Patrick Mwangi; Kamuti, Ireri; Rimberia, Jane
    The action of projective general group on the cosets of its maximal subgroups has been studied. For instance, [9] studied the action of G on the cosets of PGL(2; e) when q is an odd prime power of e. In this paper, we determine the rank and subdegrees of the action of PGL(2; q) on the cosets of its subgroup PGL(2; e) for odd q and an even power of e. We apply the table of marks to achieve this.
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    Ranks and Subdegrees of External Direct Product of Cn Dr Acting on X Y
    (UoEm, 2020) Mutua, Felix Mutinda; Kamaku, Peter Waweru; Kimani, Patrick Mwangi
    In this paper, transitivity, ranks and subdegrees of the action of ex- ternal direct product of Cyclic and Dihedral group on Cartesian Product of two sets are determined. The action is proved to be transitive. Also, it's established that the rank associated with the action is n( r+1 2 ) and subdegrees are [1][n] and [2][n( r􀀀1 2 )] when r is old. Additionally, the rank of the action for the case where r is even is proved to be n( r+2 2 ) and subdegrees are [1][2n] and [2][n( r􀀀2 2 )].