A note on the Gröbner-Shirshov bases over ad-hoc extensions of groups

Abstract

The main goal of this paper is to obtain (non-commutative) Gr?bner-Shirshov bases for monoid presentations of the knit product of cyclic groups and the iterated semidirect product of free groups. Each of the results 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.