Combinatorial group theory | Computational group theory | Combinatorics on words

Nielsen transformation

In mathematics, especially in the area of abstract algebra known as combinatorial group theory, Nielsen transformations, named after Jakob Nielsen, 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,. They were introduced in to prove that every subgroup of a free group is free (the Nielsen–Schreier theorem), but are now used in a variety of mathematics, including computational group theory, k-theory, and knot theory. The textbook devotes all of chapter 3 to Nielsen transformations. (Wikipedia).

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Related pages

Nielsen–Schreier theorem | Word problem for groups | Whitehead torsion | Combinatorial group theory | K-theory | Free group | Automorphism group of a free group | Knot (mathematics) | Finitely generated group | Trivial group | Finitely presented group | Finite group | Frattini subgroup | Random walk | Mathematics | Coxeter group | Markov chain | Subgroup | Abstract algebra | Automorphism group | Andrews–Curtis conjecture | Computational group theory | Module (mathematics) | Knot theory