Some of our results apply to local reductive IND groups G in general that is to arbi ily direct limits for interconnected reductive linear algebraic groups. Worth noting Claude Chevalley gave a complete classification of reductive groups over an algebraic closed field: They are determined by root data. Especially simple groups are over an algebraic closed field K classified up to quotas of the final central Subgruppordningar of their Dynkin chart. At that time no special use was made by the fact that the group structure can be defined by polynomials i.e. these are algebraic groups. Since homomorphism F: g m g m defined by X x p induces an isomorphism of abstract groups K K but F is not an isomorphism of algebraic groups since X 1 p is not a normal function . Some of our results apply to locally reductive ind-groups G in general i.e. to arbi y direct limits of connected reductive linear algebraic groups.Remarkably Claude Chevalley gave a complete classification of the reductive groups over an algebraically closed field: they are determined by root data.In particular simple groups over an algebraically closed field k are classified up to quotients by finite central subgroup schemes by their Dynkin diagrams.At that time no special use was made of the fact that the group structure can be defined by polynomials that is that these are algebraic groups.Then the homomorphism f: G m G m defined by x x p induces an isomorphism of abstract groups k k but f is not an isomorphism of algebraic groups because x 1 p is not a regular function .