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.
"A criterion for $c$-capability of pairs of groups." Tbilisi Math. J. 5 (1) 31 - 38, 2012. https://doi.org/10.32513/tbilisi/1528768887