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

Abstract

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.