It is well known that in a commutative Noetherian ring \(R\), every proper ideal has a reduced primary decomposition. Also if \(R\) is a commutative ring with identity and if \(B\) is an \(R\)-module satisfying the A.C.C. on its submodules, then every proper submodule of \(B\) has a reduced primary decomposition. These primary decomposition theorems are also obtained in the theory of near-rings. C. Santhakumari [J. Aust. Math. Soc., Ser. A 33, 167-170 (1982; Zbl 0491.16032)] introduced a class of near-rings called \(Q\)-near rings and proved that in a \(Q\)-near-ring with identity satisfying A.C.C. on ideals, every ideal has a primary decomposition. The first author [Indian J. Pure Appl. Math. 15, 127-130 (1984; see the preceding review Zbl 0860.16033)] proved that in a Noetherian near-ring \(N\) satisfying \(a\in Na\) for all \(a\in N\) and every left \(N\)-subgroup of \(N\) is an ideal of \(N\), every ideal has a primary decomposition. In this paper we find a class of \(N\)-groups and obtain the primary decomposition theorems for those \(N\)-groups.