Title of article :
On the converse of Baer's theorem for generalizations of groups with trivial Frattini subgroups
Author/Authors :
Taghavi, Yasaman Department of Pure Mathematics - Ferdowsi University of Mashhad, Iran , Kayvanfar orcid, Saeed Department of Pure Mathematics - Ferdowsi University of Mashhad, Iran , Chakaneh, Marzieh Department of Pure Mathematics - Ferdowsi University of Mashhad, Iran
Abstract :
In 2012, Guo and Gong proved that if G is a finite nonabelian group with Φ(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.
Keywords :
Baer's theorem , Frattini subgroup , Upper and lower central series
Journal title :
Astroparticle Physics
