Abstract
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
.