A note on growth sequences of alternating groups

Abstract.

The aim of this paper is to give a lower bound for h(2, A _n ), where h(2, A _n ) is the maximum number such that $A_n^{h(2, A_n)}$ can be generated by 2 elements, where A _n is the alternating group on n symbols, and $n \geqq 5$. Kantor and Lubotzky (1990) gave a lower bound¶$\frac{n!}{8}$ for sufficiently large n by the probability of generating the symmetric group. I have improved the above lower bound to $\frac{n!}{5}$ for large n, using a different method.