The Study About The Sum Of Elements Orders Of Finite Groups Of The Same Order

Let G be a finite group of order n and denote (G)the sum of elementorders of G. In this paper, we investigate the value of on finite groups of thesame order using the relevant theory of finite groups on the basis of the study aboutthe sum of elements orders on finite groups of the same order. The whole paper hasbeen divided into four chapters:In the first chapter, we gives a briefly review about the history of development offinite groups’ arithmetic property that impact on the structure of finite groups and thevalue of on finite groups of the same order, also gives a brief introduction aboutthe main work.In the second chapter, some number theory results and lemmas are given.In the third chapter, we systematically study the second largest value of onfinite groups of the same order and give the isomorphic class of these groups with thesecond largest value of on finite groups of the same order.In the forth chapter, we study the minimum value of on finite groups of thesame special order and give the isomorphic class of these groups with the minimumvalue of on finite groups of the same special order. In the end, we give aconjecture about symmetric groupsS non the basis of the results we have achieved.