Subgroup conjugacy separability of free-by-finite groups

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• 作者：S. C. Chagas ; P. A. Zalesskii
• 关键词：20E26 ; 20E18 ; Subgroup conjugacy separability ; Conjugacy separability
• 刊名：Archiv der Mathematik
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：104
• 期：2
• 页码：101-109
• 全文大小：197 KB
• 参考文献：1. O. Bogopolski and F. Grunewald, On subgroup conjugacy separability in the class of virtually free groups, Max-Planck-Institute of Mathematics Preprint Series, n. 110 (2010), 18 pages. p://arxiv.org/abs/1012.5122" class="a-plus-plus">arXiv:1012.5122.
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8938

文摘

A group G is said to be conjugacy subgroup separable if for every pair of non-conjugate finitely generated subgroups H and K of G, there exists a finite quotient of G where the images of these subgroups are not conjugate. The notion was introduced recently by O. Bogopolski and F. Grunewald. We prove here that finitely generated free-by-finite groups are subgroup conjugacy separable. This generalizes Theorem 1.5 in Bogopolski and Grunewald (On subgroup conjugacy separability in the class of virtually free groups, vol 110, 18 pages, 2010). We also show that free products preserve subgroup conjugacy separability. The methods are based on the profinite version of Bass–Serre’s theory of groups acting on trees. In particular, we use essentially the results of Ribes and Zalesskii (Rev Mat Iberoam 30:165-90, 2014).