Transitivity and Imprimitivity of Product of Three Alternating Groups on Cartesian Product of Three Sets of Ordered Quadruples

Abstract

In this paper, we determine the transitivity and primitivity of the product of three alternating groups acting on the cartesian product of three sets of ordered quadruples. When 𝑛 ≥ 6 and using the Orbit-Stabilizer theorem, the action has been determined to be transitive and using the definition of primitivity and blocks, the action has been determined to be imprimitive.