Moses, M. K.Nyaga, L. N.Sammy, M. W.2025-05-152025-05-152021Moses, M. K., Sammy, M. W., & Nyaga, L. N. (2021). Transitivity Action of the Cartesian Product of the Alternating Group Acting on a Cartesian Product of Ordered Sets of Triples.https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&q=Transitivity+Action+of+the+Cartesian+Product+of+the+Alternating+Group+Acting+on+a+Cartesian+Product+of+Ordered+Sets+of+Triples&btnG=#d=gs_cit&t=1747302976567&u=%2Fscholar%3Fq%3Dinfo%3AiChNyRX3cfUJ%3Ascholar.google.com%2F%26output%3Dcite%26scirp%3D0%26hl%3Denhttps://repository.chuka.ac.ke/handle/123456789/18053Research ArticleIn 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.enOrbitsStabilizerTransitivity ActionOrdered Sets of TriplesCartesian ProductFixed Point.Article