A note on test elements for monomorphisms of free groups

Dongxiao Zhao, Qiang Zhang
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Abstract

A word in a group is called a test element if any endomorphism fixing it is necessarily an automorphism. In this note, we give a sufficient condition in geometry to construct test elements for monomorphisms of a free group, by using the Whitehead graph and the action of the free group on its Cayley graph.
关于自由群单态检验元素的说明
群中的一个词,如果固定它的内态性必然是自态性,则称为检验元。在本注释中,我们给出了一个充分条件,即利用怀特海图和自由群对其凯利图的作用,在几何学中构造自由群中单态的检验元。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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