Transitivity Action of the Cartesian Product of the Alternating Group Acting on a Cartesian Product of Ordered Sets of Triples

Transitivity Action of the Cartesian Product of the Alternating Group Acting on a Cartesian Product of Ordered Sets of Triples Maraka K. Moses Musundi W. Sammy Lewis N. Nyaga

In this paper, we investigate some transitivity action properties of the cartesian product of the alternating group \(A_{n}(n \geq 5)\) acting on a cartesian product of ordered sets of triples using the Orbit-Stabilizer Theorem by showing that the length of the orbit \((p, s, v) \text { in } A_{n} \times A_{n} \times A_{n},(n \geq 5)\) acting on \(P^{[3]} \times S^{[3]} \times V^{[3]}\) is equivalent to the cardinality of \(P^{[3]} \times S^{[3]} \times V^{[3]}\) to imply transitivity.
12 24 2021 53 62 10.9734/arjom/2021/v17i1230348 https://journalarjom.com/index.php/ARJOM/article/view/519 https://www.journalarjom.com/index.php/ARJOM/article/download/30348/56946 https://www.journalarjom.com/index.php/ARJOM/article/download/30348/56946 https://www.journalarjom.com/index.php/ARJOM/article/download/30348/56947