Abstract:
The problems of existence and uniqueness of computable numberings are fundamental in theory of
computably numbered groups. In connection with the development of the theory of algorithms a study of
the problems of computability of important classes of algebraic systems are currently relevant.
Groups of unitriangular matrices over the ring are a classic representative of the class of
nilpotent groups and have numerous applications both in group theory and in its applications. In
this paper we obtain a criterion of computability of subgroups of the group of all unitriangular
matrices U Tn(K) over a computable associative ring with unity.
