群的完全嵌入

IF 0.6 4区数学 Q3 MATHEMATICS Bulletin of the Australian Mathematical Society Pub Date : 2024-01-26 DOI:10.1017/s0004972723001442

MARTIN R. BRIDSON, HAMISH SHORT

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引用次数: 0

摘要

每个可数群 G 都可以嵌入一个有限生成的群 $G^*$，而这个群是跳化的和完全的，也就是说，$G^*$ 有微不足道的中心，并且每个外变 $G^*\to G^*$ 都是一个内自变。$G^*$ 的每个有限子群都与 G 的一个有限子群共轭。如果 G 有一个有限的呈现（分别是有限的分类空间），那么 $G^*$ 也是如此。我们对 $G^*$ 的构造依赖于非对称和非哈肯的封闭双曲 3-manifolds。

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COMPLETE EMBEDDINGS OF GROUPS

Every countable group G can be embedded in a finitely generated group

$G^*$

that is hopfian and complete, that is,

$G^*$

has trivial centre and every epimorphism

$G^*\to G^*$

is an inner automorphism. Every finite subgroup of

$G^*$

is conjugate to a finite subgroup of G. If G has a finite presentation (respectively, a finite classifying space), then so does

$G^*$

. Our construction of

$G^*$

relies on the existence of closed hyperbolic 3-manifolds that are asymmetric and non-Haken.

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来源期刊

Bulletin of the Australian Mathematical Society 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

149

审稿时长

4-8 weeks

期刊介绍： Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way. Published Bi-monthly Published for the Australian Mathematical Society

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