On restriction of characters to defect groups

Giannelli, Eugenio; Sambale, Benjamin

doi:10.1016/j.jalgebra.2019.07.011

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2021

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Cited by 2 publications

(2 citation statements)

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“…Using Kessar-Malle's theorem [15] on the height zero conjecture, Giannelli-Navarro [9, Theorem C] have shown that Corollary 2 remains true for arbitrary groups G whenever P is abelian (here Q can be chosen as a defect group of the block containing χ). The next corollary settles the open question in [10] mentioned above. If true, Conjecture 4 would generalize the Brauer-Nesbitt theorem on character of p-defect 0.…”

Section: Introductionsupporting

confidence: 59%

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Restrictions of characters in p-solvable groups

Rossi¹,

Sambale²

2021

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Let G be a p-solvable group, P ≤ G a p-subgroup and χ ∈ Irr(G) such that χ(1) p ≥ |G : P | p . We prove that the restriction χ P is a sum of characters induced from subgroups Q ≤ P such that χ(1) p = |G : Q| p . This generalizes previous results by Giannelli-Navarro and Giannelli-Sambale on the number of linear constituents of χ P . We provide some evidence for the statement above being true for arbitrary groups. This can be seen as an extension of Brauer-Nesbitt's theorem on characters of p-defect zero. It also extends a conjecture of Wilde.

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Section: Introductionsupporting

confidence: 59%

“…In a subsequent paper [10], Giannelli and the second author studied the following blockwise version of the conjecture. Let B be a p-block of G with defect group D. Let χ ∈ Irr(B) be of positive height and assume that χ D has a linear constituent.…”

Section: Introductionmentioning

confidence: 99%