Abstract:
In 1961 G. Higman proved a remarkable theorem establishing a deep connection between the
logical notion of recursiveness and questions about finitely presented groups.
The basic aim of the present paper is to provide the reader with a rigorous and detailed proof
of Higman's Theorem. All the necessary preliminary material, including elements of group theory
and recursive functions theory, is systematically presented and with complete proofs. The aquainted
reader may skip the first sections and proceed immediately to the last.
