Abstract
We construct uncountably categorical 3-nilpotent groups of exponent p > 3. They are not one-based and do not allow the interpretation of an infinite field. Therefore they are counterexamples to Zilbers Conjecture. First 2-nilpotent new uncoutably categorical groups were contructed in [3]. Here we use the method of the additive Collapse developed in [5]. Essentially we work with 3-nilpotent graded Lie algebras over the field with p elements.
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