Higman operations on integer sequences, and embeddings of recursive groups

This is an extended version of summary of the talk at the International Conference on Group Theory in honor of Victor Mazurov on the occasion of his 80th birthday. The concise version of this report can be found in the talks and communications band at the Conference site. The objective of the current talk is to present our very recent article in which we for various types of recursive groups discuss possibility of their explicit embeddings into finitely presented groups.