Signature for piecewise continuous groups

IF 0.6 3区数学 Q3 MATHEMATICS

Groups Geometry and Dynamics Pub Date : 2020-02-28 DOI:10.4171/ggd/664

Octave Lacourte

引用次数: 2

Abstract

Let PC be the group of bijections from [0, 1[ to itself which are continuous outside a finite set. Let PC be its quotient by the subgroup of finitely supported permutations. We show that the Kapoudjian class of PC vanishes. That is, the quotient map PC $\rightarrow$ PC splits modulo the alternating subgroup of even permutations. This is shown by constructing a nonzero group homomorphism, called signature, from PC to Z 2Z. Then we use this signature to list normal subgroups of every subgroup G of PC which contains S fin and such that G, the projection of G in PC , is simple.

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分段连续群的签名

设PC是[0,1中的一组双射[在有限集外是连续的。设PC是它与有限支持的置换子群的商。我们证明了PC的Kapoudjian类是消失的。也就是说，商映射PC$\rightarrow$PC模分解偶数置换的交替子群。这通过构造一个非零群同态来证明，称为签名，从PC到Z2Z。然后我们使用这个签名列出包含S fin的PC的每个子群G的正规子群，使得G，G在PC中的投影，是简单的。

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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来源期刊

Groups Geometry and Dynamics 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Groups, Geometry, and Dynamics is devoted to publication of research articles that focus on groups or group actions as well as articles in other areas of mathematics in which groups or group actions are used as a main tool. The journal covers all topics of modern group theory with preference given to geometric, asymptotic and combinatorial group theory, dynamics of group actions, probabilistic and analytical methods, interaction with ergodic theory and operator algebras, and other related fields. Topics covered include: geometric group theory; asymptotic group theory; combinatorial group theory; probabilities on groups; computational aspects and complexity; harmonic and functional analysis on groups, free probability; ergodic theory of group actions; cohomology of groups and exotic cohomologies; groups and low-dimensional topology; group actions on trees, buildings, rooted trees.