Action type geometrical equivalence of representations of groups

Abstract

In the paper we prove (Theorem 8.1) that there exists a continuum of non isomorphic simple modules over KF₂, where F₂ is a free group with 2 generators (compare with [Ca] where a continuum of non isomorphic simple 2-generated groups is constructed). Using this fact we give an example of a non action type logically Noetherian representation (Section 9).