Periodic and finite groups, embeddings and identities

We plan to build such a 3-generator group in which the identity x^n=1 is a probabilistic identity but not an identity in the usual sense, to show that there exists a continuum of non-isomorphic 4-generator groups, in which the identity x^n=1 is a probabilistic identity but not an identity in the usual sense, to construct torsion-free non-cyclic and non-simple groups which have a total dominating set consisting of a finite number of elements, to obtain an explicite embedding of the group Q into a finitely presented group, more generally, to suggest a constructive method for explicite embeddings of recursive groups into finitely presented groups, to study the effect of Higman operations on the sequences, to build embeddings of groups with different properties, to prove that the Majorana axiomatics best describes the Monster algebra and the Monster group for which the «Straight Flush» hypothesis will be verified for all the finite simple groups, we also plan to describe the multiplicative semigroup of an associative, commutative ring with identity, from which we can obtain the description of the multiplicative group of a skew fields as a special case.