Products of subgroups, subnormality, and relative orders of elements

IF 0.6 3区数学 Q3 MATHEMATICS

Ars Mathematica Contemporanea Pub Date : 2022-10-05 DOI:10.26493/1855-3974.2975.1b2

Luca Sabatini

引用次数: 0

Abstract

Let $G$ be a group. We give an explicit description of the set of elements $x \in G$ such that $x^{|G:H|} \in H$ for every subgroup of finite index $H \leqslant G$. This is related to the following problem: given two subgroups $H$ and $K$, with $H$ of finite index, when does $|HK:H|$ divide $|G:H|$?

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元素的子群、次正规和相对序的乘积

让$G$成为一个团体。我们给出了元素集合$x \in G$的显式描述，使得$x^{|G:H|} \in H$对于有限索引$H \leqslant G$的每一子群。这涉及到以下问题:给定两个子群$H$和$K$, $H$的索引是有限的，$|HK:H|$何时能除$|G:H|$ ?

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

Ars Mathematica Contemporanea MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Ars mathematica contemporanea will publish high-quality articles in contemporary mathematics that arise from the discrete and concrete mathematics paradigm. It will favor themes that combine at least two different fields of mathematics. In particular, we welcome papers intersecting discrete mathematics with other branches of mathematics, such as algebra, geometry, topology, theoretical computer science, and combinatorics. The name of the journal was chosen carefully. Symmetry is certainly a theme that is quite welcome to the journal, as it is through symmetry that mathematics comes closest to art.