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About: Nielsen transformation     Goto   Sponge   NotDistinct   Permalink

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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.