Gröbner-Shirshov bases for special extensions of groups

Abstract

The main goal of this paper is to obtain (non-commutative) Gröbner-Shirshov bases for monoid presentations of the central extention of groups, the knit product of cyclic groups and the iterated semidirect product of free groups. Each of the results in here will give a new algorithm for getting normal forms of the elements of these groups, and hence a new algorithm for solving the word problem over them.