kimani, Gachago jN, Kinyanjui J.j, Rimberiakimani, Patrickmuchemi, Jacob kiboi2024-06-062024-06-062015ISSN 2224-5804 (Paper)ISSN 2225-0522 (Online)http://repository.embuni.ac.ke/handle/embuni/4350ArticleIn this paper, we study some transitivity action properties of the alternating group An(n=4,5,6,7 ,) acting on unordered and ordered pairs from the set X = {1,2,...,n} 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] . key words : Orbits ,alternating group An , An on unordered and ordered quadruples from the set X.enOrbitsalternating group AnAn on unorderedordered quadruples from the set XArticle