Congruences associated with families of nilpotent subgroups and a theorem of Hirsch

IF 0.8 4区数学 Q2 MATHEMATICS

Comptes Rendus Mathematique Pub Date : 2023-11-10 DOI:10.5802/crmath.514

Stefanos Aivazidis, Thomas Müller

引用次数: 0

Abstract

Our main result associates a family of congruences with each suitable system of nilpotent subgroups of a finite group. Using this result, we complete and correct the proof of a theorem of Hirsch concerning the class number of a finite group of odd order.

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幂零子群族的同余及赫希定理

我们的主要结果将同余族与有限群的幂零子群的每一个合适系统联系起来。利用这一结果，完成并修正了关于奇阶有限群类数的Hirsch定理的证明。

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

Comptes Rendus Mathematique 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

115

审稿时长

16.6 weeks

期刊介绍： The Comptes Rendus - Mathématique cover all fields of the discipline: Logic, Combinatorics, Number Theory, Group Theory, Mathematical Analysis, (Partial) Differential Equations, Geometry, Topology, Dynamical systems, Mathematical Physics, Mathematical Problems in Mechanics, Signal Theory, Mathematical Economics, … Articles are original notes that briefly describe an important discovery or result. The articles are written in French or English. The journal also publishes review papers, thematic issues and texts reflecting the activity of Académie des sciences in the field of Mathematics.