TRANSITIVITY ACTION OF THE CARTESIAN PRODUCT OF THE ALTERNATING GROUP ACTING ON A CARTESIAN PRODUCT OF ORDERED SETS OF TUPLES

Abstract

Transitivity action properties of the alternating group An on ordered and unordered n - tuples and on the direct product of alternating group on unordered sets have been greatly studied by different researchers. However, no work has been done for transitivity action of the Cartesian product of the alternating group on the Cartesian product of ordered n - tuples of sets. This paper determined the transitivity action of the Cartesian product of the alternating group acting on a Cartesian product of ordered sets of triples. The Orbit-Stabilizer Theorem has been used to determine the transitivity action. When n >_ 5 , the action of the Cartesian product of alternating group on the Cartesian product of ordered sets of triples is transitive.