Malle–Robinson conjecture on the number of irreducible Brauer characters

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Let HH be a finite group, let BB be an ellell-block of HH, and let DD be a defect group of BB. The sectional ellell-rank s(D)s(D) is the maximum of the ranks of elementary abelian ellell-sections of DD. Malle–Robinson conjecture. One has

l(B)≤ℓs(D).l(B) \leq \ell^{s(D)}.

This conjecture bounds the number l(B)l(B) of irreducible Brauer characters in a block by a quantity determined by the sectional ellell-rank of its defect group. Its resolution status is not specified in the source.

References

Primary source

Ruwen Hollenbach, “On e-cuspidal pairs of finite groups of exceptional Lie Type”, arXiv:1905.10754 (2021).

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