Broué's isotypy conjecture for the sporadic groups and their covers and automorphism groups

Sambale, Benjamin

doi:10.1142/s0218196715500277

Cited by 5 publications

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References 44 publications

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“…The sporadic and the Tits groups can be checked with [GAP] (or one appeals to the Alperin weight conjecture proved in [Sam2]).…”

Section: Proofs Of Theorem 11 and Theorem 12mentioning

confidence: 99%

Bounding p-Brauer characters in finite groups with two conjugacy classes of p-elements

Hung,

Sambale,

Tiep

2024

Isr. J. Math.

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Let k(B0) and l(B0) respectively denote the number of ordinary and p-Brauer irreducible characters in the principal block B0 of a finite group G. We prove that, if k(B0)−l(B0) = 1, then l(B0) ≥ p − 1 or else p = 11 and l(B0) = 9. This follows from a more general result that for every finite group G in which all non-trivial p-elements are conjugate, l(B0) ≥ p − 1 or else p = 11 and $$G/{{\bf{O}}_{{p^\prime }}}(G) \cong C_{11}^2\, \rtimes\,{\rm{SL}}(2,5)$$ G / O p ′ ( G ) ≅ C 11 2 ⋊ SL ( 2 , 5 ) . These results are useful in the study of principal blocks with few characters.We propose that, in every finite group G of order divisible by p, the number of irreducible Brauer characters in the principal p-block of G is always at least $$2\sqrt {p - 1} + 1 - {k_p}(G)$$ 2 p − 1 + 1 − k p ( G ) , where kp(G) is the number of conjugacy classes of p-elements of G. This indeed is a consequence of the celebrated Alperin weight conjecture and known results on bounding the number of p-regular classes in finite groups.

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“…The sporadic and the Tits groups can be checked with [GAP] (or one appeals to the Alperin weight conjecture proved in [Sam2]).…”

Section: Proofs Of Theorem 11 and Theorem 12mentioning

confidence: 99%

Bounding p-Brauer characters in finite groups with two conjugacy classes of p-elements

Hung,

Sambale,

Tiep

2024

Isr. J. Math.

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On Blocks with Abelian Defect Groups of Small Rank

Sambale

2016

Results Math

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Loewy lengths of centers of blocks

Külshammer

Sambale

2018

The Quarterly Journal of Mathematics

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Let B be a block of a finite group with respect to an algebraically closed field F of characteristic p > 0. In a recent paper, Otokita gave an upper bound for the Loewy length LL(ZB) of the center ZB of B in terms of a defect group D of B. We refine his methods in order to prove the optimal bound LL(ZB) ≤ LL(F D) whenever D is abelian. We also improve Otokita's bound for non-abelian defect groups. As an application we classify the blocks B such that LL(ZB) ≥ |D|/2.

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Broué's isotypy conjecture for the sporadic groups and their covers and automorphism groups

Cited by 5 publications

References 44 publications

Bounding p-Brauer characters in finite groups with two conjugacy classes of p-elements

Bounding p-Brauer characters in finite groups with two conjugacy classes of p-elements

On Blocks with Abelian Defect Groups of Small Rank

Loewy lengths of centers of blocks

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