فهرست نشریات علمی دسترسی آزاد ایران

In 2012, Guo and Gong proved that if $G$ is a finite nonabelian group with $\Phi(G)=1$, then $|G:Z(G)|<|G'||U(G)|$, in which $U(G)$ is the nilpotent residual of $G$. We show that the assumption of finiteness of the group can be omitted. Moreover, we investigate converse of Schur and Baer's theorems for groups that can be seen as  generalizations of groups with trivial Frattini subgroups  and state some properties of $n$-isoclinism families  of these groups.