MORE FRAÏSSÉ LIMITS OF NILPOTENT GROUPS OF FINITE EXPONENT

The class of nilpotent groups of class c and prime exponent p > c with additional predicates Pc ⊆Pc−1 ⊆ . . . ⊆P1 for suitable subgroups has the amalgamation property. Hence the Fräıssé limit D of the finite groups of this class exists. 〈1〉⊆Pc(D)⊆ . . . ⊆P2(D)⊆P1(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 א0-categorical. For c = 2 this was proved by Baudisch in Bull. London Math. Soc. 33 (2001) 513–519.