p-groups with all the elements of order p in the center

Resting on a suitable base of the quotients of the lambda-series for the free groups on r generators, we get, for p odd, a class of TH-p-groups (n)G(r) with arbitrary large derived length. We prove that every TH-p-group G with r generators and exponent p(n) is a quotient of (n)G(r) and a product of m cyclic groups, where p(m) = Omega(1)(G)\. At last we describe the TH-p-groups of exponent p(2).