In 1990 , Bhattacharya and Mukherjee defined the notion of ?- pair for a maximal subgroup of a finite group. Then Zhao, in 1995 proved that for any maximal subgroup M of a finite group G, there exists a normal maximal ?-pair related to M.
A group G is called n?-pair if | (G)| = n, in which (G) denotes the set of all ?-pairs of G. In this paper, we show that G is 1?-pair if and only if G is a cyclic group of prime power order. Also, it is shown that there is no 2?-pair finite group.
1991 Mathematics Subject Classification: 20E34, 20D10.