Wreath 积与自由可解群中共轭问题的几何
群论
2013-07-26 v1
摘要
我们描述了共轭问题的一个有效版本，并针对 Wreath 积和自由可解群对其进行了研究。该问题涉及估计群中两个元素之间短共轭元的长度，这一概念引出了共轭长度函数的定义。我们证明了对于自由可解群，其共轭长度函数至多为三次方。对于 Wreath 积，其行为取决于所涉及两个群的共轭长度函数，以及商群内的子群扭曲。
引用
@article{arxiv.1307.6812,
title = {The Geometry of the Conjugacy Problem in Wreath Products and Free Solvable Groups},
author = {Andrew W. Sale},
journal= {arXiv preprint arXiv:1307.6812},
year = {2013}
}
备注
24 pages, 4 figures. This was formed from the splitting of arXiv:1202.5343, titled "On the Magnus Embedding and the Conjugacy Length Function of Wreath Products and Free Solvable Groups," into two papers. The contents of this paper remain largely unchanged