On the structure of the commutator subgroup of certain homeomorphism groups

被引：3
作者：
Michalik, Ilona [1 ]
Rybicki, Tomasz [1 ]
机构：
[1] AGH Univ Sci & Technol, Fac Appl Math, PL-30059 Krakow, Poland
来源：
TOPOLOGY AND ITS APPLICATIONS | 2011年 / 158卷 / 11期
关键词：
Group of homeomorphisms; Factorizable group; Commutator subgroup; Perfectness; Uniform perfectness; Simplicity; Uniform simplicity; Open manifold; LIPSCHITZ HOMEOMORPHISMS; DIFFEOMORPHISMS; FOLIATION; PERFECT;
D O I：
10.1016/j.topol.2011.05.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An important theorem of Ling states that if G is any factorizable non-fixing group of homeomorphisms of a paracompact space then its commutator subgroup [G, G] is perfect. This paper is devoted to further studies on the algebraic structure (e.g. uniform perfectness, uniform simplicity) of [G, G] and [(G) over tilde, (G) over tilde], where (G) over tilde is the universal covering group of G. In particular, we prove that if G is a bounded factorizable non-fixing group of homeomorphisms then [G, G] is uniformly perfect (Corollary 3.4). The case of open manifolds is also investigated. Examples of homeomorphism groups illustrating the results are given. (C) 2011 Elsevier B.V. All rights reserved.
引用
收藏
页码：1314 / 1324
页数：11
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