ON THE GROUPS SATISFYING THE CONVERSE OF SCHUR''S THEOREM

Abstract. a famous theorem of schur states that for a group g finiteness of g=z(g) implies thefiniteness of g0: the converse of schur's theorem is an interesting problem which has been consideredby some authors. recently, podoski and szegedy proved the truth of the converse of schur's theoremfor 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 satisfythe converse of schur's theorem and at the same time admit the podoski and szegedy's bound as theupper bound for the index of their centers.