The Decision Problems for Properties of Transformation Groups

Abstract:

      In this paper the fundamental result about the decision problems for properties-of FRT-groups (i. e. the groups each of which is isomorphic with a group generated by a finite number of recursive transformations) has been proved: Let p be any algebraic property for groups such that there is a FRT -group G₁ which has the property p, a FRT-group G₂ which has not the property p, and G₂ is not isomorphic with any subgroup of any FRT-group which has the property p. Then the problem of deciding, for any given groap P genetated by a finite number of recursive transformations, whether or not the group G isomorphic with P has the property p is unsolvable.