Nielsen transformation
In mathematics, especially in the area of modern algebra known as combinatorial group theory, Nielsen transformations are certain automorphisms of a free group which are a non-commutative analogue of row reduction and one of the main tools used in studying free groups (Fine, Rosenberger & Stille 1995). Given a finite basis of a free group F n {\displaystyle F_{n}} , the corresponding set of elementary Nielsen transformations forms a finite generating set of A u t ( F n ) {\displaystyle \mathrm {Aut} (F_{n})} .