On a conjecture of G. Malle and G. Navarro on nilpotent blocks.
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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.
DOI :
10.37236/704
Classification :
20C30, 20C20, 05E10
Mots-clés : height zero characters, nilpotent blocks, defect groups, spin-blocks, covering groups, alternating groups, representations, symmetric groups, bar-partitions
Mots-clés : height zero characters, nilpotent blocks, defect groups, spin-blocks, covering groups, alternating groups, representations, symmetric groups, bar-partitions
@article{10_37236_704,
author = {Jean-Baptiste Gramain},
title = {On a conjecture of {G.} {Malle} and {G.} {Navarro} on nilpotent blocks.},
journal = {The electronic journal of combinatorics},
year = {2011},
volume = {18},
number = {1},
doi = {10.37236/704},
zbl = {1230.20011},
url = {http://geodesic.mathdoc.fr/articles/10.37236/704/}
}
Jean-Baptiste Gramain. On a conjecture of G. Malle and G. Navarro on nilpotent blocks.. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/704
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