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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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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Test Elements of Polynomial and Free Associative Algebrasalgebra freely generated by a set . = {., ... , .}. The general problem under discussion in this chapter is how to recognize automorphisms of .[.] and .<.>. Following van den Essen and Shpilrain [124], we give the following definitions.

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Alexander A. Mikhalev,Vladimir Shpilrain,Jie-Tai YIncludes supplementary material:

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