The essential rank of classical groups

Let G be a finite classical group defined over a finite field with odd characteristic. Let r>2 be a prime, not dividing the characteristic, and D⩽G a Sylow r-subgroup. We consider the Frobenius category FD(G) and determine the cardinality of a minimal conjugation family for it. This amounts to de...

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Bibliographic Details
Published in:Journal of algebra 2012-03, Vol.354 (1), p.148-157
Main Authors: An, Jianbei, Dietrich, Heiko
Format: Article
Language:English
Subjects:
Classical groups
Conjugation families
Essential rank
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Summary:Let G be a finite classical group defined over a finite field with odd characteristic. Let r>2 be a prime, not dividing the characteristic, and D⩽G a Sylow r-subgroup. We consider the Frobenius category FD(G) and determine the cardinality of a minimal conjugation family for it. This amounts to determining the number of G-conjugacy classes of essential subgroups of D, that is, the essential rank of FD(G). In addition, we characterise those classical groups which allow an r-local subgroup controlling r-fusion.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2011.12.022