More Fraisse limits of nilpotent groups of finite exponent

The class of nilpotent groups of class c and prime exponent p > c with additional predicates P-c subset of or equal to Pc-1 subset of or equal to ... subset of or equal to P-1 for suitable subgroups has the amalgamation property. Hence the Fraisse limit D of the finite groups of this class exists. <1> subset of or equal to P-c (D) subset of or equal to ... subset of or equal to P-2(D) subset of or equal to P-1(D) = D is the lower and the upper central series of D. In this extended language, D is ultrahomogeneous. The elementary theory of D allows the elimination of quantifiers and it is No-categorical. For c = 2 this was proved by Baudisch in Bull. London Math. Soc. 33 (2001) 513-519.