We prove that if G is a finite group in which the elements of the same order outside the center are conjugate, then either G is abelian or G ≌ S3.
Xing-zhong YOU~1 Guo-hua QIAN~2 Wu-jie SHI~(3+) ~1 School of Mathematics and Computing Science,Changsha University of Science and Technology,Changsha 410076,China
Let G be a finite p-group.If the order of the derived subgroup of each proper subgroup of G divides pi,G is called a Di-group.In this paper,we give a characterization of all D1-groups.This is an answer to a question introduced by Berkovich.
