11.78 (1990)

An isomorphism of groups of points of algebraic groups is called semialgebraic if it can be represented as a composition of an isomorphism of translation of the field of definition and a rational morphism.
$\qquad$ a) Is it true that the existence of an isomorphism of groups of points of two directly undecomposable algebraic groups with trivial centres over an algebraically closed field implies the existence of a semialgebraic isomorphism of the groups of points?
$\qquad$ b) Is it true that every isomorphism of groups of points of directly undecomposable algebraic groups with trivial centres defined over algebraic fields is semialgebraic? A field is called algebraic if all its elements are algebraic over the prime subfield.