Browsing by Author "Kamuti, Ireri"

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    On the cycle indices of frobenious groups
    (2010) Munywoki, Michael; Kamuti, Ireri; Kivunge, Benard
    There are several very useful formulas, which give the cycle indices of the binary operation of the sum, product, composition and po wer group of M and H in terms of cycle indices of M and H . One very useful binary operation on groups, which has not been exploited, is the semidirect product. Suppose G = M ⋊ H , a semi direct product; the question is: how can we express the cycle index of G in terms of the cycle indices of M and H ? This work partially answers this question by considering the cycle indices of so me particularly semidirect product groups; namely – Frobenious groups
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    Suborbits and Suborbital Graphs of the Symmetric Group acting on Ordered r-element Subsets
    (2013) Rimberia, Jane; Kamuti, Ireri; Kivunge, Bernard; Kinyua, Francis
    The ranks and subdegrees of the symmetric group n S acting on [ ] r X , the set of all ordered r -element subsets from X have been studied (See Rimberia [4]). In this pape r, we examine some properties of suborbits and suborbital graphs of n S acting on [ ] r X