Cossey's conjecture on lifts of irreducible Brauer characters

Let pp be a prime, let GG be a pp-solvable group, and let φIBr(G)\varphi\in\operatorname{IBr}(G) be an irreducible Brauer character. A lift of φ\varphi is a character χIrr(G)\chi\in\operatorname{Irr}(G) whose restriction χ0\chi^0 to the pp-regular elements of GG equals φ\varphi, and let LφL_\varphi be the set of all lifts. If QQ is a vertex for φ\varphi in the sense of Green, Cossey's conjecture.

LφQ:Q.|L_\varphi|\leq |Q:Q'|.

This conjecture generalizes the known bound in the normal-vertex case and is established when QQ is abelian, but its general status is not specified in the source.

Sources & referencesView supporting material

Primary source

Junwei Zhang, Xuewu Chang and Ping Jin, “Counting lifts of irreducible Brauer characters”, arXiv:2502.05771 (2025).

Additional references

2 papers in this index state this conjecture (2023–2025). The statement above is taken from the most recent of them; the others are arXiv:2301.12408.

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