The notion of capability for pairs of groups was defined by Ellis in 1996. In this paper, we extend the theory of c-capability for pairs of groups and introduce a criterion, denoted by Z_c^*(G,N), for c-capability of a pair (G,N) of groups. We also study the behavior of
Z_c^*(G,N) with respect to direct products of groups.

Tbilisi Mathematical Journal, Vol. 5(1) (2012), pp. 31-38