Taghavi, Y., Kayvanfar, S., Chakaneh, M. (2019). On the converse of Baer's theorem for generalizations of groups with trivial Frattini subgroups. Algebraic Structures and Their Applications, 6(1), 139-148. doi: 10.29252/as.2019.1396

Yasaman Taghavi; Saeed Kayvanfar; Marzieh Chakaneh. "On the converse of Baer's theorem for generalizations of groups with trivial Frattini subgroups". Algebraic Structures and Their Applications, 6, 1, 2019, 139-148. doi: 10.29252/as.2019.1396

Taghavi, Y., Kayvanfar, S., Chakaneh, M. (2019). 'On the converse of Baer's theorem for generalizations of groups with trivial Frattini subgroups', Algebraic Structures and Their Applications, 6(1), pp. 139-148. doi: 10.29252/as.2019.1396

Taghavi, Y., Kayvanfar, S., Chakaneh, M. On the converse of Baer's theorem for generalizations of groups with trivial Frattini subgroups. Algebraic Structures and Their Applications, 2019; 6(1): 139-148. doi: 10.29252/as.2019.1396

On the converse of Baer's theorem for generalizations of groups with trivial Frattini subgroups

^{}Department of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran

Abstract

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.

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