Universal theory of the class of finite nilpotent groups is unsolvable

Abstract

Kargapolov [i, Problem 1.25] posed the problem of the solvability of the universal theory of the class of finite groups and the class of finite nilpotent groups. Slobodskoi [2] recently proposed a construction that would allow him to deduce a negative answer for the class of finite groups. Using some of the ideas of his construction, we will give here the solution to the problem for the class of finite nilpotent groups. The main result of our paper is the following