Abstract
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 χP 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 χP. Although this statement does not hold for arbitrary groups, we conjecture a weaker version which 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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