 Tietze transformations

A Tietze transformation changes a group presentation without changing the presented group, by adding or removing a consequence of the relators, or by adding or eliminating a generator together with a defining equation expressing it in the others. For example a generator $t$ defined by $t=xs{x}^{-1}$ can be eliminated by substitution in every remaining relator.

Tietze transformations are a method in topology used to extend a continuous function defined on a subspace of a topological space to the whole space.