Transitivity Action of An on (n=4,5,6,7) on Unordered and Ordered Quadrupples

In this paper, we study some transitivity action properties of the alternating group �� �� (�� =4,5,6,7 ,) acting on unordered and ordered pairs from the set �� = {1,2,…,�� } through determination of the number of disjoint equivalence classes called orbits.when n≤ 7 ,the alternating group acts transitively on both X (4) and X [4] .