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The essential rank of Brauer categories for finite groups of Lie type
Author(s) -
An Jianbei,
Dietrich Heiko
Publication year - 2013
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bds095
Subject(s) - mathematics , sylow theorems , rank (graph theory) , block (permutation group theory) , combinatorics , lie group , type (biology) , pure mathematics , finite group , group (periodic table) , chemistry , ecology , biology , organic chemistry
Let G be a finite group of Lie type in characteristic p . Let B be a p ‐block of G with non‐trivial Sylow B ‐subgroup ( D , b D ). We consider the Brauer categoryℱ ( D , b D )( G , B )and determine its essential rank. In addition, we characterize those finite groups G of Lie type that admit a p ‐local subgroup that controls B ‐fusion.