Neostability-properties of Fraïssé limits of 2-nilpotent groups of exponent $${p > 2}$$p>2

Let $${L(n)}$$L(n) be the language of group theory with n additional new constant symbols $${c_1,\ldots,c_n}$$c1,…,cn. In $${L(n)}$$L(n) we consider the class $${{\mathbb{K}}(n)}$$K(n) of all finite groups G of exponent $${p > 2}$$p>2, where $${G'\subseteq\langle c_1^G,\ldots,c_n^G\rangle \subseteq Z(G)}$$G′⊆⟨c1G,…,cnG⟩⊆Z(G) and $${c_1^G,\ldots,c_n^G}$$c1G,…,cnG are linearly independent. Using amalgamation we show the existence of Fraïssé limits $${D(n)}$$D(n) of $${{\mathbb{K}}(n)}$$K(n). $${D(1)}$$D(1) is Felgner’s extra special p-group. The elementary theories of the $${D(n)}$$D(n) are supersimple of SU-rank 1. They have the independence property.