Transitivity of the Product Action of Finite Alternating Groups on Cartesian Product of Finite Ordered Sets 0f γTuples

Abstract

In this paper, we determine the transitivity of the product action of finite alternating groups on the Cartesian product of finite ordered sets of 𝜸- tuples. Transitivity action has been determined using the Orbit-stabilizer theorem, by showing that the length of the orbit (𝒑𝟏, 𝒑𝟐, 𝒑𝟑, … , 𝒑𝒎−𝟏, 𝒑𝒎) in 𝑨𝒏𝟏 × 𝑨𝒏𝟐 × … × 𝑨𝒏𝒎−𝟏 × 𝑨𝒏𝒎 , (𝒏 − 𝜸 ≥ 𝟐) acting on 𝑷𝟏 [𝜸] × 𝑷𝟐 [𝜸] × … × 𝑷𝒎−𝟏 [𝜸] × 𝑷𝒎 [𝜸] is equivalent to the cardinality of 𝑷𝟏 [𝜸] × 𝑷𝟐 [𝜸] × … × 𝑷𝒎−𝟏 [𝜸] × 𝑷𝒎 [𝜸] to imply transitivity.