On the frobenius group

It is proved that forl > 1 the permutational rank of a Frobenius group with kernel of nilpotency class 1 is greater than 4^i–1+1. Let p and q be prime numbers, q¦p – 1, 1 < j < q. For all such p, q, j one constructs Frobenius groups of order p^{j + 1}q with kernel of nilpotency class j and order p^j+1. For p=7, q=3, j =2 we obtain O. Yu. Shmidt's known example.Deceased.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, Nos. 7 and 8, pp. 1021–1030, July–August, 1991.