arXiv 1012.35532010-12-16math.RTmath.GR

Conjectures of Alperin and Broue for 2-blocks with elementary abelian defect groups of order 8

Radha Kessar, Shigeo Koshitani, Markus Linckelmann

备注：: 40 pages

英文摘要：

Using the classification of finite simple groups we prove Alperin's weight conjecture and the character theoretic version of Broue's abelian defect group conjecture for 2-blocks of finite groups with an elementary abelian defect group of order 8.

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

Broué's Conjecture for 2-blocks with elementary abelian defect groups of order 32

The first author has recently classified the Morita equivalence classes of 2-blocks B of finite groups with elementary abelian defect group of order 32. In all but three cases he proved that the Morita equivalence class determines the inertial quotient of B. We finish the remaining cases by utilizing the theory of lower defect groups. As a corollary, we verify Broué's Abelian Defect Group Conjecture in this situation.

2020-11-13math.GRmath.RT

On saturated fusion systems and Brauer indecomposability of Scott modules

Let $p$ be a prime number, $G$ a finite group, $P$ a $p$-subgroup of $G$ and $k$ an algebraically closed field of characteristic $p$. We study the relationship between the category $\Ff_P(G)$ and the behavior of $p$-permutation $kG$-modules with vertex $P$ under the Brauer construction. We give a sufficient condition for $\Ff_P(G)$ to be a saturated fusion system. We prove that for Scott modules with abelian vertex, our condition is also necessary. In order to obtain our results, we prove a criterion for the categories arising from the data of $(b, G)$-Brauer pairs in the sense of Alperin-Brou…

2010-09-13math.ATmath.GRmath.RT

Modular representations of finite groups and Lie theory

This article discusses the modular representation theory of finite groups of Lie type from the viewpoint of Broue's abelian defect group conjecture. We discuss both the defining characteristic case, the inspiration for Alperin's weight conjecture, and the non-defining case, the inspiration for Broue's conjecture. The modular representation theory of general finite groups is conjectured to behave both like that of finite groups of Lie type in defining characteristic, and in non-defining characteristic, to a large extent. The expected behaviour of modular representation theory of finite groups o…

2022-11-01math.RT

Broué's abelian defect group conjecture holds for the Harada-Norton sporadic simple group $HN$

In representation theory of finite groups, there is a well-known and important conjecture due to M. Broué. He conjectures that, for any prime $p$, if a $p$-block $A$ of a finite group $G$ has an abelian defect group $P$, then $A$ and its Brauer corresponding block $B$ of the normaliser $N_G(P)$ of $P$ in $G$ are derived equivalent (Rickard equivalent). This conjecture is called Broué's abelian defect group conjecture. We prove in this paper that Broué's abelian defect group conjecture is true for a non-principal 3-block $A$ with an elementary abelian defect group $P$ of order 9 of the Harada-N…

2009-06-28math.RT

Broué's abelian defect group conjecture holds for the sporadic simple Conway group Co_3

In the representation theory of finite groups, there is a well-known and important conjecture due to M. Broué. He conjectures that, for any prime p, if a p-block A of a finite group G has an abelian defect group P, then A and its Brauer corresponding block A_N of the normaliser N_G(P) of P in G are derived equivalent (Rickard equivalent). This conjecture is called Strong Version of Broué's Abelian Defect Group Conjecture. In this paper, we prove that the strong version of Broué's abelian defect group conjecture is true for the non-principal 2-block A with an elementary abelian defect group P o…

2011-09-12math.RT

Broué's abelian defect group conjecture holds for the double cover of the Higman-Sims sporadic simple group

In the representation theory of finite groups, there is a well-known and important conjecture, due to Broué saying that for any prime p, if a p-block A of a finite group G has an abelian defect group P, then A and its Brauer corresponding block B of the normaliser N_G(P) of P in G are derived equivalent. We prove in this paper, that Broué's abelian defect group conjecture, and even Rickard's splendid equivalence conjecture are true for the faithful 3-block A with an elementary abelian defect group P of order 9 of the double cover 2.HS of the Higman-Sims sporadic simple group. It then turns out…

2012-06-02math.RT

更多相关论文收起更多论文

关于主块的 Héthelyi-Külshammer 猜想

On Héthelyi-Külshammer's conjecture for principal blocks

本文证明了有限群主 $p$-块中不可约常特征标数至少为 $2\sqrt{p-1}$，从而证实 Héthelyi-Külshammer 猜想并肯定回答有界亏群主块的 Brauer 问题 21。

2021-02-18math.GRmath.RT

Morita equivalence classes of 2-blocks of defect three

We give a complete description of the Morita equivalence classes of blocks with elementary abelian defect groups of order 8 and of the derived equivalences between them. A consequence is the verification of Broué's abelian defect group conjecture for these blocks. It also completes the classification of Morita and derived equivalence classes of 2-blocks of defect at most three defined over a suitable field.

2014-09-22math.RT