Geometrical equivalence and action type geometrical equivalence of group representations

Abstract

In this paper we construct an example of two representations \((V_{1},G_{1})\) and \((V_{2},G_{2})\) which are action type geometrically equivalent and groups \(G_{1}\) and \(G_{2}\) are geometrically equivalent, but the representations \((V_{1},G_{1})\) and \((V_{2},G_{2})\) are not geometrically equivalent.