Asian Journal of Pure and Applied Mathematics

One of the important problems in finite groups theory is group characterization by speceific property. Properties, such as element order, the set of element with the same order, the largest element order, etc. Next, on of the methods is group characterization by using the order of the group and the number of elements of order p, where p the largest prime divisor of |G|. For this purpose, in this paper, discuss about conjecture of Moreto' on finite simple groups. In other words, we prove that suzuki groups Sz(q), where q = 2²ⁿ⁺¹ , n ≥ 1 and p is the largest prime divisor of |Sz(q)|, can be uniquely determined by the |Sz(q)| and |S(p)|, where |S(p)| is the order the largest prime divisor of the suzuki groups Sz(q).