Abstract:
In this paper, we study some transitivity action properties of the alternating group 𝐴𝑛(𝑛=5,6,7 ,8) acting on unordered and ordered pairs from the set 𝑋𝑋 = {1,2,β¦,𝑛𝑛} through determination of the number of disjoint equivalence classes called orbits. When 𝑛𝑛β€ 8, the alternating group acts transitively on both X (2) and X[2]. Mathematics Subject Classification: 20BO5, 06A75, 06F15.