Extensions of nilpotent blocks

1990 ◽  
Vol 102 (1) ◽  
pp. 17-71 ◽  
Author(s):  
Burkhard K�lshammer ◽  
Lluis Puig
Keyword(s):  
Nilpotent Blocks

scholarly journals Nilpotent Blocks of Quasisimple Groups for the Prime Two

2011 ◽  
Vol 16 (1) ◽  
pp. 1-28 ◽  
Author(s):  
Jianbei An ◽  
Charles William Eaton
Keyword(s):  
Nilpotent Blocks

scholarly journals Block Extensions, Local Categories and Basic Morita Equivalences

2020 ◽  
Vol 71 (2) ◽  
pp. 703-728
Author(s):  
Tiberiu Coconeţ ◽  
Andrei Marcus ◽  
Constantin-Cosmin Todea
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Cohomology Class ◽  
Group Extension ◽  
Modular System ◽  
Pointed Group ◽  
A Finite Group ◽  
Nilpotent Blocks ◽  
The Way

Abstract Let $(\mathcal{K},\mathcal{O},k)$ be a $p$-modular system where $p$ is a prime and $k$ algebraically closed, let $b$ be a $G$-invariant block of the normal subgroup $H$ of a finite group $G$, having defect pointed group $Q_\delta$ in $H$ and $P_\gamma$ in $G$ and consider the block extension $b\mathcal{O}G$. One may attach to $b$ an extended local category $\mathcal{E}_{(b,H,G)}$, a group extension $L$ of $Z(Q)$ by $N_G(Q_\delta )/C_H(Q)$ having $P$ as a Sylow $p$-subgroup, and a cohomology class $[\alpha ]\in H^2(N_G(Q_\delta )/QC_H(Q),k^\times )$. We prove that these objects are invariant under the $G/H$-graded basic Morita equivalences. Along the way, we give alternative proofs of the results of Külshammer and Puig (1990), and Puig and Zhou (2012) on extensions of nilpotent blocks. We also deduce by our methods a result of Zhou (2016) on $p^{\prime}$-extensions of inertial blocks.

scholarly journals On Nilpotent Blocks of Finite Groups

1994 ◽  
Vol 163 (1) ◽  
pp. 128-134 ◽  
Author(s):  
A. Watanabe
Keyword(s):  
Finite Groups ◽  
Nilpotent Blocks

scholarly journals On the sources of simple modules in nilpotent blocks

2008 ◽  
Vol 319 (11) ◽  
pp. 4559-4574 ◽  
Author(s):  
Adam Salminen
Keyword(s):  
Simple Modules ◽  
Nilpotent Blocks

Extensions of nilpotent blocks over arbitrary fields

2008 ◽  
Vol 261 (2) ◽  
pp. 351-371
Author(s):  
Yuanyang Zhou
Keyword(s):  
Nilpotent Blocks

scholarly journals On a Conjecture of G. Malle and G. Navarro on Nilpotent Blocks

10.37236/704 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Jean-Baptiste Gramain
Keyword(s):  
Finite Group ◽  
Recent Article ◽  
Simple Groups ◽  
Alternating Group ◽  
Covering Group ◽  
Group 2 ◽  
A Finite Group ◽  
Nilpotent Blocks

In a recent article, G. Malle and G. Navarro conjectured that the $p$-blocks of a finite group all of whose height 0 characters have the same degree are exactly the nilpotent blocks defined by M. Broué and L. Puig. In this paper, we check that this conjecture holds for spin-blocks of the covering group $2.{\mathfrak A}_n$ of the alternating group ${\mathfrak A}_n$, thereby solving a case excluded from the study of quasi-simple groups by Malle and Navarro.

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