On Fundamental Group of a Certain Class of Welded Knots

被引：0

作者：

Li Zhi-guo ^{[1
,2
]}

Lei Feng-chun ^{[1
]}

Chen Zhi ^{[3
]}

Wu Jie ^{[4
]}

机构：

[1] Department of Mathematics, Dalian University of Technology

[2] School of Science, Hebei University of Technology

[3] Department of Mathematics, Hefei University of Technology

[4] Department of Mathematics, National University of Singapore

来源：

Communications in Mathematical Research | 2017年 / 33卷 / 02期

关键词：

welded knot; fundamental group; Dihedral group; linear group;

D O I：

10.13447/j.1674-5647.2017.02.09

中图分类号：

O152 [群论];

学科分类号：

070104 ;

摘要：

In this paper, a certain class of welded knots K;is considered. By calculating the commutators subgroup of fundamental group Gn of welded knot K;,n ∈ Z;, we show that these welded knots are not equivalent to each other and they are all not classical knots. Secondly, we study some properties of Gn and obtain that Gn is linear, residually finite and Hopfian.

引用

页码：177 / 184

页数：8

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