on the converse of baer's theorem for generalizations of groups with trivial frattini subgroups

In 2012, guo and gong proved that if $g$ is a finite nonabelian group with $phi(g)=1$, then $|g:z(g), in which u(g) is the nilpotent residual of g. we show that the assumption of niteness 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.