会犯错误
发表于 2025-3-25 06:12:44
Schulze-Makuch Dirk,Louis N. IrwinBy refining the methods of the previous chapter, we obtain another bound for the number of characters in a block of a finite group. This time the fusion system of the block will play an essential role. The statement of the result differs in case . = 2 from the odd case.
enterprise
发表于 2025-3-25 11:05:22
An Overview of Cosmic EvolutionAfter proving a strong version of Alperin’s Fusion Theorem, we derived some properties of essential subgroups in fusion systems. By using the classification of the strongly .-embedded subgroups we restrictions on the automorphism groups of essential subgroups. This leads to consequences in small cases.
FEIGN
发表于 2025-3-25 12:35:56
Open ConjecturesWe introduce a list of open conjectures about block theory of finite groups. The first of these conjectures was proposed in 1954 by Brauer, and the last one of our list is a conjecture by Gluck from 2011. It also includes famous conjectures by Olsson, Alperin, McKay and others. All of these conjectures will be considered in the following chapters.
Irrigate
发表于 2025-3-25 16:18:47
Quadratic FormsWe introduce a quadratic form arising from the Cartan matrix of a block of a finite group. By invoking Brauer’s notion of basic sets, we exploit some properties of the quadratic form with will lead to restriction on the number of characters of the block. We also discuss a question about the indecomposability of Cartan matrices.
LATE
发表于 2025-3-25 22:11:11
A Bound in Terms of Fusion SystemsBy refining the methods of the previous chapter, we obtain another bound for the number of characters in a block of a finite group. This time the fusion system of the block will play an essential role. The statement of the result differs in case . = 2 from the odd case.
荣幸
发表于 2025-3-26 04:03:12
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Arb853
发表于 2025-3-26 04:37:55
Blocks of Finite Groups and Their Invariants978-3-319-12006-5Series ISSN 0075-8434 Series E-ISSN 1617-9692
Corroborate
发表于 2025-3-26 09:27:29
Marie-Pierre Callait,Dominique Gauthier of groups algebras, (lower) defect groups, the Brauer homomorphism, decomposition numbers, subsections, and fusion systems. Moreover, we present Brauer’s three main theorems as well as a few other important results. Most theorems are given without proof.
哄骗
发表于 2025-3-26 13:26:19
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让你明白
发表于 2025-3-26 16:55:04
J. Rivera Islas,J. C. Micheau,T. Buhseonly. Most importantly, we introduce Fong’s reductions. In the second part we recall the classification of the finite simple groups and note some well-known results about representation theory of simple groups. Finally, we consider the .-solvable case.