Let Gbe a p-solvable group, P <= Ga p-subgroup and chi is an element of Irr(G) such that chi(1)(p) >=vertical bar G : P vertical bar(p). We prove that the restriction chi P is a sum of characters induced from subgroups Q = Psuch that chi(1)(p)=vertical bar G : Q vertical bar(p). This generalizes previous results by Giannelli-Navarro and Giannelli-Sambale on the number of linear constituents of chi P. 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. (C) 2021 Elsevier Inc. All rights reserved.
Rossi, D., Sambale, B. (2021). Restrictions of characters in p-solvable groups. JOURNAL OF ALGEBRA, 587, 130-141 [10.1016/j.jalgebra.2021.07.034].
Restrictions of characters in p-solvable groups
Rossi, D;
2021
Abstract
Let Gbe a p-solvable group, P <= Ga p-subgroup and chi is an element of Irr(G) such that chi(1)(p) >=vertical bar G : P vertical bar(p). We prove that the restriction chi P is a sum of characters induced from subgroups Q = Psuch that chi(1)(p)=vertical bar G : Q vertical bar(p). This generalizes previous results by Giannelli-Navarro and Giannelli-Sambale on the number of linear constituents of chi P. 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. (C) 2021 Elsevier Inc. All rights reserved.File | Dimensione | Formato | |
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