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

Abstract

In this paper, we investigate the primitivity action properties of the cartesian product of an alternating

group

𝐴 (𝑛≥5) 𝑛

acting on a cartesian product of ordered sets of triples using the definition primitivity

and blocks. When

𝑛≥5, the cartesian product of the alternating group,

𝐴 × 𝐴 × 𝐴 𝑛 𝑛 𝑛

, acts imprimitively on a cartesian product of ordered sets of triples, [3] [3] [3].