Details
| Original language | English |
|---|---|
| Pages (from-to) | 130-141 |
| Number of pages | 12 |
| Journal | Journal of algebra |
| Volume | 587 |
| Early online date | 19 Aug 2021 |
| Publication status | Published - 1 Dec 2021 |
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 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. 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.
Keywords
- Character restriction, Linear constituents, p-solvable groups
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Journal of algebra, Vol. 587, 01.12.2021, p. 130-141.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Restrictions of characters in p-solvable groups
AU - Rossi, Damiano
AU - Sambale, Benjamin
N1 - Funding Information: We thank Gabriel Navarro for sharing his insights on a previous version of this paper, and for requesting more computer checking. We appreciate Eugenio Giannelli's effort to prove corresponding results for symmetric groups. Moreover, Alexander Hulpke has kindly provided an updated database [12] of all perfect groups of order at most 10 6 . Thomas Breuer has introduced the authors to numerous tricks regarding character tables in GAP. The first author is supported by the research training group GRK2240 : Algebro-geometric Methods in Algebra, Arithmetic and Topology of the German Research Foundation . The second author is supported by the German Research Foundation ( SA 2864/1-2 and SA 2864/3-1 ).
PY - 2021/12/1
Y1 - 2021/12/1
N2 - 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. 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.
AB - 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. 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.
KW - Character restriction
KW - Linear constituents
KW - p-solvable groups
UR - http://www.scopus.com/inward/record.url?scp=85113357274&partnerID=8YFLogxK
U2 - 10.1016/j.jalgebra.2021.07.034
DO - 10.1016/j.jalgebra.2021.07.034
M3 - Article
VL - 587
SP - 130
EP - 141
JO - Journal of algebra
JF - Journal of algebra
SN - 0021-8693
ER -