University of IsfahanInternational Journal of Group Theory2251-76501420121201On the groups satisfying the converse of Schur's theorem17148510.22108/ijgt.2012.1485ENAzamKaheniDepartment of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, IranRasoulHatamianDepartment of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, IranSaeedKayvanfarDepartment of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, IranJournal Article20120512A famous theorem of Schur states that for a group $G$ finiteness of $G/Z(G)$ implies the finiteness of $G'.$ The converse of Schur's theorem is an interesting problem which has been considered by some authors. Recently, Podoski and Szegedy proved the truth of the converse of Schur's theorem for capable groups. They also established an explicit bound for the index of the center of such groups. This paper is devoted to determine some families of groups among non-capable groups which satisfy the converse of Schur's theorem and at the same time admit the Podoski and Szegedy's bound as the upper bound for the index of their centers.https://ijgt.ui.ac.ir/article_1485_97332f3127ba88174f99b39be512bb8a.pdf