The commutator subgroup of a pair of groups

H. Arabyani

Schur proved that if G is a group such that G/Z(G) is finite, then G' is finite. Several authors studied the converse of Schur's theorem. In this paper, we extend the converse of Schur's theorem to a pair of groups. Also, we determine the structure of a pairs of groups under some conditions. 

Tbilisi Mathematical Journal, Vol. 14(3) (2021), pp. 171-177