On the Ranks of the Alternating Group An.

Let G be a finite group and X be a conjugacy class of G. The rank of X in G, denoted by rank(G : X), is defined to be the minimal number of elements of X generating G. In this paper we establish some general results on the ranks of certain conjugacy classes of elements for simple alternating group A n . We apply these general results together with the structure constants method to determine the ranks of all the non-trivial classes of A 8 and A 9 . [ABSTRACT FROM AUTHOR]