On G-Conjugacy Class Sizes of Some p-Regular Element in a Normal Subgroup

Let N0 be a p-solvable normal group of a finite group G,and mn≠1 be two coprime positive integers.The purpose of this article is to show that a p-complement of N0/N0∩Z(G) is either a prime power order group or a solvable Frobenius group under the condition that the G-conjugacy class size of p-regular primary element and biprimary element in N0 is 1,n or m.