TY - JOUR
ID - 1485
TI - On the groups satisfying the converse of Schur's theorem
JO - International Journal of Group Theory
JA - IJGT
LA - en
SN - 2251-7650
AU - Kaheni, Azam
AU - Hatamian, Rasoul
AU - Kayvanfar, Saeed
AD - Department of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, Iran
Y1 - 2012
PY - 2012
VL - 1
IS - 4
SP - 1
EP - 7
KW - Capable group
KW - n-isoclinism
KW - Extra special p-group
KW - Schur's theorem
DO - 10.22108/ijgt.2012.1485
N2 - A 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.
UR - https://ijgt.ui.ac.ir/article_1485.html
L1 - https://ijgt.ui.ac.ir/article_1485_97332f3127ba88174f99b39be512bb8a.pdf
ER -