arXiv math/02104052002-10-25math.ATmath.GR

Non-simple localizations of finite simple groups

José L. Rodríguez, Jérôme Scherer, Antonio Viruel

备注：: 10 pages
发表信息：: J. of Algebra 305 (2006), 765-774
DOI：: 10.1016/j.jalgebra.2006.06.041

英文摘要：

Often a localization functor (in the category of groups) sends a finite simple group to another finite simple group. We study when such a localization also induces a localization between the automorphism groups and between the universal central extensions. As a consequence we exhibit many examples of localizations of finite simple groups which are not simple.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

On localizations of quasi-simple groups with given countable center

A group homomorphism $i: H \to G$ is a localization of $H$ if for every homomorphism $φ: H\rightarrow G$ there exists a unique endomorphism $ψ: G\rightarrow G$, such that $i ψ=φ$ (maps are acting on the right). Göbel and Trlifaj asked in \cite[Problem 30.4(4), p. 831]{GT12} which abelian groups are centers of localizations of simple groups. Approaching this question we show that every countable abelian group is indeed the center of some localization of a quasi-simple group, i.e. a central extension of a simple group. The proof uses Obraztsov and Ol'shanskii's construction of infinite simple gr…

2020-11-29math.ATmath.GR

Finite simple groups and localization

The purpose of this paper is to explore the concept of localization, which comes from homotopy theory, in the context of finite simple groups. We give an easy criterion for a finite simple group to be a localization of some simple subgroup and we apply it in various cases. Iterating this process allows us to connect many simple groups by a sequence of localizations. We prove that all sporadic simple groups (except possibly the Monster) and several groups of Lie type are connected to alternating groups. The question remains open whether or not there are several connected components within the f…

2001-10-02math.ATmath.GR

Cohn localization of finite group rings

The purpose of this paper is to give a complete description of the Cohn localization of the augmentation map $Z[G]\rightarrow Z$ when $G$ is any finite group.

2016-08-19math.AT

Group localization and two problems of Levine

A. K. Bousfield's $H\mathbb Z$-localization of groups inverts homologically two-connected homomorphisms of groups. J. P. Levine's algebraic closure of groups inverts homomorphisms between finitely generated and finitely presented groups which are homologically two-connected and for which the image normally generates. We resolve an old problem concerning Bousfield $H\mathbb Z$-localization of groups, and answer two questions of Levine regarding algebraic closure of groups. In particular, we show that the kernel of the natural homomorphism from a group $G$ to it's Bousfield $H\mathbb Z$-localiza…

2013-06-25math.ATmath.GR

Codimension 2 embeddings and finite localization of spaces

In order to classify concordance classes of codimension 2 embeddings in a manifold M, we need to determine the complement of such an embedding. These complements are spaces over M well defined up to some homology equivalence. We construct a localization functor corresponding to this class of homology equivalences and we give a characterization of local objects in terms of homotopy groups.

2021-10-27math.AT

On lengths of HZ-localization towers

In this paper, the $H\mathbb Z$-length of different groups is studied. By definition, this is the length of $H\mathbb Z$-localization tower or the length of transfinite lower central series of $H\mathbb Z$-localization. It is proved that, for a free noncyclic group, its $H\mathbb Z$-length is $\geq ω+2$. For a large class of $\mathbb Z[C]$-modules $M,$ where $C$ is an infinite cyclic group, it is proved that the $H\mathbb Z$-length of the semi-direct product $M\rtimes C$ is $\leq ω+1$ and its $H\mathbb Z$-localization can be described as a central extension of its pro-nilpotent completion. In …

2016-06-27math.ATmath.GR

更多相关论文收起更多论文

Equivariant chromatic localizations and commutativity

In this paper, we study the extent to which Bousfield and finite localizations relative to a thick subcategory of equivariant finite spectra preserve various kinds of highly structured multiplications. Along the way, we describe some basic, useful results for analyzing categories of acyclics in equivariant spectra, and we show that Bousfield localization with respect to an ordinary spectrum (viewed as an equivariant spectrum with trivial action) always preserves equivariant commutative ring spectra.

2017-08-09math.AT

将有限 Reedy 范畴呈现为有限直范畴的局部化

Presentation of finite Reedy categories as localizations of finite direct categories

本文通过构造直范畴 Down(C) 及其到 Reedy 范畴 C 的函子，将有限 Reedy 范畴呈现为有限直范畴的 (∞,1)-范畴局部化，从而为同伦类型论的有限截断单纯类型元理论提供工具。

2025-02-07math.ATmath.CTmath.LO

A note on localizations of mapping spaces

We show that if A is a simply connected, finite, pointed CW-complex then the mapping spaces Map(A, -) are preserved by the localization functors only if A has the rational homotopy type of a wedge of spheres of a fixed dimension.

2008-08-04math.AT