Browsing by Author "Nyaga, L. N."

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    Primitivity Action of the Cartesian Product of an Alternating Group Acting on a Cartesian Product of Ordered Sets of Triples
    (London Journals Press, 2022) Maraka, M. K.; Musundi, S. W.; Nyaga, L. N.
    In this paper, we investigate the primitivity action properties of the cartesian product of an alternating group 𝐴 (𝑛≥5) 𝑛 acting on a cartesian product of ordered sets of triples using the definition primitivity and blocks. When 𝑛≥5, the cartesian product of the alternating group, 𝐴 × 𝐴 × 𝐴 𝑛 𝑛 𝑛 , acts imprimitively on a cartesian product of ordered sets of triples, , [3] [3] [3]. Mathematics Subject Classification: 20B05; 20B15; 20B20
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    Transitivity Action of the Cartesian Product of the Alternating Group Acting on a Cartesian Product of Ordered Sets of Triples
    (2021) Moses, M. K.; Nyaga, L. N.; Sammy, M. W.
    In this paper, we investigate some transitivity action properties of the cartesian product of the alternating group 𝐴𝑛(𝑛 ≥ 5) acting on a cartesian product of ordered sets of triples using the Orbit-Stabilizer Theorem by showing that the length of the orbit (𝑝, 𝑠, 𝑣) in 𝐴𝑛 × 𝐴𝑛 × 𝐴𝑛, (𝑛 ≥ 5) acting on 𝑃[3] × 𝑆[3] × 𝑉[3] is equivalent to the cardinality of 𝑃[3] × 𝑆[3] × 𝑉[3] to imply transitivity.
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    TRANSITIVITY ACTION OF THE CARTESIAN PRODUCT OF THE ALTERNATING GROUP ACTING ON A CARTESIAN PRODUCT OF ORDERED SETS OF TUPLES
    (Chuka University, 2022) Maraka, M. K.; Musundi, S. M.; Nyaga, L. N.
    Transitivity action properties of the alternating group An on ordered and unordered n - tuples and on the direct product of alternating group on unordered sets have been greatly studied by different researchers. However, no work has been done for transitivity action of the Cartesian product of the alternating group on the Cartesian product of ordered n - tuples of sets. This paper determined the transitivity action of the Cartesian product of the alternating group acting on a Cartesian product of ordered sets of triples. The Orbit-Stabilizer Theorem has been used to determine the transitivity action. When n >_ 5 , the action of the Cartesian product of alternating group on the Cartesian product of ordered sets of triples is transitive.