Neostability properties of Fraisse limits of 2-nilpotent groups of exponent p > 2

TL;DR

This paper constructs Fraisse limits of certain 2-nilpotent groups with exponent p > 2, demonstrating their superstable theories of SU-rank 1, including a specific case related to Felgner's p-group.

Contribution

It introduces a new class of Fraisse limits for 2-nilpotent groups with specific properties and analyzes their model-theoretic stability and rank.

Findings

Fraisse limits D(n) have superstable theories of SU-rank 1

D(1) corresponds to Felgner's extra special p-group

Amalgamation of finite 2-nilpotent groups with specified properties

Abstract

We amalgamate finite 2-nilpotent groups G of exponent p > 2, where G' is contained in a subgroup of the center, generated by n elements. We get Fraisse limits D(n) with superstable elementary theories of SU-rank 1. D(1) is Felgner's extra special p-group.