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Nielsen Transformation: Mathematics, Abstract Algebra, Combinatorial Group Theory, Jakob Nielsen (mathematician), Gaussian Elimination, Carl Friedrich Gauss, Computational Group Theory, K-theory - Couverture souple

 
9786130331771: Nielsen Transformation: Mathematics, Abstract Algebra, Combinatorial Group Theory, Jakob Nielsen (mathematician), Gaussian Elimination, Carl Friedrich Gauss, Computational Group Theory, K-theory

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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, (Fine, Rosenberger & Stille 1995). They were introduced in (Nielsen 1921) to prove that every subgroup of a free group is free, but are now used in a variety of mathematics, including computational group theory, k-theory, and knot theory. The textbook (Magnus, Karrass & Solitar 2004) devotes all of chapter 3 to Nielsen transformations.

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