Let G be a finite non abelian group. It is proved by Qian et al. that if non central same order elements in G are conjugate,then GS3.In order to prove this theorem, the theorem for the classification of finite simple groups is used. In this paper, we discuss the proof of some special cases that Sylow 2 subgroups of G satisfy some condition without this theorem. For example, we prove that if G is a finite non abelian group with abele Sylow 2 subgroups and non central same order elements in G are conjugate, then GS3
