The same order type A5 characterizing

Abstract

This study examines the same-order type of G, suppose G be a finite group that α(G)=S_tt∈πe(G) and define nse(G) or α(G) is the same-order type whose S_t is the number of elements of order t that t∈π_e (G) and π_e (G) is the set of elements order of G. If |G|=n in G, then we say that G is α_n-group. Shin in [1] showed that every α_2-group is nilpotent and every α_3-group is solvable. In addition, the structure of the such group and proved if G be an α_n-group then |π(G)|≤n, and conjectures that if the researcher examines the same-order type of the nonabelian simple group. This study proves that if G is a simple nonabelian group, the same-order type of G has four elements if and only if G is isomorphism with A_5. This study proves that for any nonabelian simple group G, we have S_p≠S_q for odd prime divisors p and q of order of G.