Titlebook: Combinatorial Methods; Free Groups, Polynom Alexander A. Mikhalev,Vladimir Shpilrain,Jie-Tai Y Book 2004 Springer Science+Business Media Ne

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Book 2004wn as Gr?bner bases. This marked the beginning of a new, "combinatorial", era in commu- tative algebra. It is not very likely that Buchberger was directly influenced by ideas from combinatorial group theory, but his famous algorithm bears resemblance to Nielsen‘s method, although in a more sophisticated form.

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Test Elements action on a single element, a test element. More precisely: .. An element . ∈ . is called a test element (for recognizing automorphisms) of a group . if, whenever .(.) = . for an endomorphism . of ., it follows that . is an automorphism.

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Schreier Varieties of Algebrasny subalgebra of a free algebra of this variety is free in the same variety of algebras. In Section 11.1, we describe the main types of Schreier varieties and introduce universal multiplicative enveloping algebras of free algebras. Theorem 11.1.1 gives the main properties of the free algebras of the

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