Combinatorial methods: from groups to polynomial algebras
Vladimir Shpilrain
Abstract
Combinatorial methods (or methods of elementary transformations) came to group theory from low-dimensional topology in the beginning of the century. Soon after that, combinatorial group theory became an independent area with its own powerful techniques. On the other hand, combinatorial commutative algebra emerged in the sixties, after Buchberger introduced what is now known as Gröbner bases. The purpose of this survey is to show how ideas from one of those areas contribute to the other.
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