Local Structure, Vertices and Alperin's Conjecture

Robinson, Geoffrey R.

doi:10.1112/plms/s3-72.2.312

Cited by 56 publications

(73 citation statements)

References 7 publications

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“…G. Robinson [1996] remarked that as an easy consequence of finite version of the Borel-Tits Theorem, if G is a finite group with a (B, N )-pair of rank n and characteristic p, then plr(G) = n. So we can determine the p-local ranks of finite groups of Lie type directly, where p is the defining characteristic of such groups. In fact, as an easy consequence of [Gorenstein et al 1994], we have:…”

Section: For Certain Primesmentioning

confidence: 99%

“…Robinson [1996] introduced an inductive invariant known as the p-local rank to give an inductive proof of his variant of the conjecture.…”

Section: Introductionmentioning

confidence: 99%

“…Following [Robinson 1996], the p-local rank plr(G) of G is the length of a longest chain in (G). We say that a subgroup H of G is a trivial intersection (t.i.)…”

Section: Introductionmentioning

confidence: 99%

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On finite simple groups ofp-local rank two

Wang¹

2009

Pacific J. Math.

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Section: For Certain Primesmentioning

confidence: 99%

“…Robinson [1996] introduced an inductive invariant known as the p-local rank to give an inductive proof of his variant of the conjecture.…”

Section: Introductionmentioning

confidence: 99%

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On finite simple groups ofp-local rank two

Wang¹

2009

Pacific J. Math.

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“…A key observation -which is implicitly in [11] and more explicitly in [19] -is that if z(Q, e Q ) = 0 then Q is F -centric, and one easily sees that Q is also F -radical (since normal p-subgroups are contained in all defect groups). In other words, only the Fcentric radical subgroups of P are relevant for the right hand expression of Alperin's weight conjecture.…”

Section: 3mentioning

confidence: 99%

Fusion category algebras

Linckelmann

2004

Journal of Algebra

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This is the unspecified version of the paper.This version of the publication may differ from the final published version. Permanent repository link: Markus LinckelmannAbstract. The fusion system F on a defect group P of a block b of a finite group G over a suitable p-adic ring O does not in general determine the number l(b) of isomorphism classes of simple modules of the block. We show that conjecturally the missing information should be encoded in a single second cohomology class α of the constant functor with value k × on the orbit categoryF c of F-centric subgroups Q of P of b which "glues together" the second cohomology classes α(Q) of AutF (Q)

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“…Denote by R(G) the set of radical p-chains of G. Following [3] and [29], define the p-local rank to be Proof. Suppose W is a defect group of b.…”

Section: Corollary 12 Given a P-group D There Are Only Finitely Manmentioning

confidence: 99%

Blocks with trivial intersection defect groups

Eaton

2004

Math. Z.

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Abstract. We show that each block whose defect groups intersect pairwise trivially either has cyclic or generalised quaternion defect groups, or is Morita equivalent to one of a given list of blocks of central extensions of automorphism groups of non-abelian simple groups. In particular we classify all blocks of automorphism groups of non-abelian simple groups whose defect groups are non-cyclic and intersect pairwise trivially. A consequence is that Donovan's conjecture holds for blocks whose defect groups intersect pairwise trivially. Mathematics Subject Classification (2000): 20C20

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Local Structure, Vertices and Alperin's Conjecture

Cited by 56 publications

References 7 publications

On finite simple groups ofp-local rank two

On finite simple groups ofp-local rank two

Fusion category algebras

Blocks with trivial intersection defect groups

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