Brauer relations in finite groups

Bartel Alex; Dokchitser Tim

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Brauer relations in finite groups

机译：有限群中的Brauer关系

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摘要

If G is a non-cyclic finite group, non-isomorphic G-sets X, Y may give rise to isomorphic permutation representations C[X] congruent to C[Y]. Equivalently, the map from the Burnside ring to the rational representation ring of G has a kernel. Its elements are called Brauer relations, and the purpose of this paper is to classify them in all finite groups, extending the Tomehave-Bouc classification in the case of p-groups.

机译：如果G是一个非循环有限群，则非同构G集X，Y可能会产生与C [Y]一致的同构置换表示C [X]。等效地，从Burnside环到G的有理表示环的映射具有一个核。它的元素称为Brauer关系，本文的目的是在所有有限组中对它们进行分类，以扩展p组中的Tomehave-Bouc分类。

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来源
《Journal of the European Mathematical Society: JEMS》 |2015年第10期|共40页
作者
Bartel Alex; Dokchitser Tim;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Brauer relations; finite groups; permutation groups; Burnside ring; rational representations;

机译：Brauer关系;有限群;置换群;Burnside环;理性表示;

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Brauer relations in finite groups

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