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In the context of Higman embeddings of recursive groups into finitelypresented groups we suggest an algorithm which uses Higman operations toexplicitly constructs the specific recursively enumerable sets of integersequences arising during the embeddings. This makes the constructive Higmanembedding a doable task for certain wide classes of groups. Specific auxiliaryoperations are introduced to make the work with Higman operations a simpler andmore intuitive procedure. Also, an automated mechanism of constructiveembeddings of countable groups into 2-generator groups is mentioned.

The Higman operations and embeddings of recursive groups