arXiv 1702.033682017-02-11math.GR

On the problem of existence and conjugacy of injectors of generalized $π$-soluble groups

Xia Yin, Nanying Yang, N. T. Vorobev

英文摘要：

In this paper, we prove the existence and conjugacy of injectors of a generalized $π$-soluble groups for the Hartley class defined by a invariable Hartley function, and give a description of the structure of the injectors.

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

The conjugacy growth of the soluble Baumslag-Solitar groups

In this paper we give asymptotics for the conjugacy growth of the soluble Baumslag-Solitar groups $BS(1,k)$, $k\geq 2$, with respect to the standard generating set, by providing a complete description of geodesic conjugacy representatives. We show that the conjugacy growth series for these groups are transcendental, and give formulas for the series. As a result of our computation we also establish that in each $BS(1,k)$ the conjugacy and standard growth rates are equal.

2019-08-14math.GR

On F-injectors of Fitting set of a finite group

Let $G$ be some generalized $π$-soluble groups and ${\cal F}$ be a Fitting set of $G$. In this paper, we prove the existence and conjugacy of ${\cal F}$-injectors of $G$, and give a description of the structure of the injectors.

2017-02-11math.GR

Injectors in $π$-separable groups

Let $π$ be a set of primes. We show that $π$-separable groups have a conjugacy class of $\mathfrak F$-injectors for suitable Fitting classes $\mathfrak F$, which coincide with the usual ones when specializing to soluble groups.

2020-08-03math.GR

On injectors of Hartley set of a finite group

Let G be a group and H be a Hartley set of G. In this paper, we prove the existence and conjugacy of H-injectors of G and describe the structure of the injectors. As application, some known results are directly followed.

2017-07-25math.GR

A problem in the Kourovka notebook concerning the number of conjugacy classes of a finite group

In this paper, we consider Problem 14.44 in the Kourovka notebook, which is a conjecture about the number of conjugacy classes of a finite group. While elementary, this conjecture is still open and appears to elude any straightforward proof, even in the soluble case. However, we do prove that a minimal soluble counterexample must have certain properties, in particular that it must have Fitting height at least 3 and order at least 2000.

2008-10-30math.GR

可解算术群中的扭曲共轭

Twisted conjugacy in soluble arithmetic groups

本文研究可解算术群的扭曲共轭与 $R_\infty$ 性质，通过建立充分条件构造维数递增且所有自同伦等价 Nielsen 数为零的可解流形序列。

2024-10-21math.ATmath.GRmath.NT

更多相关论文收起更多论文

Twisted conjugacy in residually finite groups of finite Prüfer rank

Suppose, $G$ is a residually finite group of finite upper rank admitting an automorphism $φ$ with finite Reidemeister number $R(φ)$ (the number of $φ$-twisted conjugacy classes). We prove that such $G$ is soluble-by-finite (in other words, any residually finite group of finite upper rank, which is not soluble-by-finite, has the $R_\infty$ property). This reduction is the first step in the proof of the second main theorem of the paper: suppose, $G$ is a residually finite group of finite Prüfer rank and $φ$ is its automorphism with $R(φ)<\infty$; then $R(φ)$ is equal to the number of equivalence…

2022-10-02math.DSmath.GRmath.RT

共轭类的平方与 Baer-Suzuki 定理的一个变体

Squares of conjugacy classes and a variant on the Baer-Suzuki Theorem

本文针对有限群中阶为 $p$ 的元素构成的正规子集 $A$，证明了若 $A^2$ 均为 $p$-元素则生成子群可解，并在 $O_p(G)=1$ 条件下确定了相关群结构性质，同时给出了最优性反例。

2023-06-30math.GR

由 $p$-正则共轭类大小的不连通公因子图得到的可解性

Solubility from a disconnected common-divisor graph on $p$-regular conjugacy-class sizes

本文证明若有限群 $G$ 的 $p$-正则元素共轭类大小的公因子图不连通，则 $G$ 可解，通过构造稳定化子并利用 Dolfi-Lucido 定理与 Burnside 定理排除非阿贝尔合成因子。

2026-10-22math.GR

Classifying Spaces with Virtually Cyclic Stabilisers for Certain Infinite Cyclic Extensions

Let G be an infinite cyclic extension, 1 -> B -> G -> Z -> 1, of a group B where the action of Z on the set of conjugacy classes of non-trivial elements of B is free. This class of groups includes certain ascending HNN-extensions with abelian or free base groups, certain wreath products by Z and the soluble Baumslag-Solitar groups BS(1,m) with |m|> 1. We construct a model for Evc(G), the classifying space of G for the family of virtually cyclic subgroups of G, and give bounds for the minimum dimension of Evc(G). We construct a 2-dimensional model for Evc(G) where G is a soluble Baumslag-Solita…

2010-07-03math.ATmath.GR