The equation w(x, y) = u over free groups: an algebraic approach
The equation w(x, y) = u over free groups: an algebraic approach
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自由群上的方程 w(x, y) = u：代数方法
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发表时间：
2007
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通讯作者：
Nicholas W. M. Touikan
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作者：
Nicholas W. M. Touikan
利用Kharlampovich和Miasnikov发展的理论，并独立地由Sela描述从有限生成群G到自由群F的同态集，我们描述了形式为w(x，y)=u的方程的解，其中u位于F中，且w(x，y)是{x，y}±1中的一个词。我们还给出了一个仅用一个自同构的‘水平’来描述其解的例子。
Abstract Using the theory developed by Kharlampovich and Miasnikov, and independently by Sela, to describe the set of homomorphisms from a finitely generated group G into a free group F, we describe the solutions to equations of the form w(x, y) = u with coefficients from F and unknowns x, y, where u lies in F and w(x, y) is a word in {x, y}±1. We also give an example of a single equation whose solutions cannot be described with only one ‘level’ of automorphisms.