Finite Groups in Which the Orders of Elements Are Continuous Integers

R.Brandl has put the following question:Whether for any positive integer nthere exists a finite group such that the orders of all elements are ≤n and foreach m≤n there exists an element of order m.We call such finite groups OC_ngroups.B.H.Neumann has studied such general groups with n≤3.For all n≤7such finite groups、exist.For example,the alternating group A_7 is an OC_7 group. In this paper we mainly prove the following two theorems.