Details
| Original language | English |
|---|---|
| Article number | 107227 |
| Journal | Journal of Pure and Applied Algebra |
| Volume | 227 |
| Issue number | 3 |
| Early online date | 30 Aug 2022 |
| Publication status | Published - Mar 2023 |
Abstract
Dade's conjecture predicts that if p is a prime, then the number of irreducible characters of a finite group of a given p-defect is determined by local subgroups. In this paper we replace p by a set of primes π and prove a π-version of Dade's conjecture for π-separable groups. This extends the (known) p-solvable case of the original conjecture and relates to a π-version of Alperin's weight conjecture previously established by the authors.
Keywords
- Alternating sums, Dade's conjecture, π-subgroups
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Journal of Pure and Applied Algebra, Vol. 227, No. 3, 107227, 03.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Alternating sums over π-subgroups
AU - Navarro, Gabriel
AU - Sambale, Benjamin
N1 - Funding Information: We thank the anonymous referee for drawing our attention to a theorem of Quillen. The research of the first author is supported by Ministerio de Ciencia e Innovación PID2019-103854GB-I00 . The second author thanks the German Research Foundation (projects SA 2864/1-2 and SA 2864/3-1 ).
PY - 2023/3
Y1 - 2023/3
N2 - Dade's conjecture predicts that if p is a prime, then the number of irreducible characters of a finite group of a given p-defect is determined by local subgroups. In this paper we replace p by a set of primes π and prove a π-version of Dade's conjecture for π-separable groups. This extends the (known) p-solvable case of the original conjecture and relates to a π-version of Alperin's weight conjecture previously established by the authors.
AB - Dade's conjecture predicts that if p is a prime, then the number of irreducible characters of a finite group of a given p-defect is determined by local subgroups. In this paper we replace p by a set of primes π and prove a π-version of Dade's conjecture for π-separable groups. This extends the (known) p-solvable case of the original conjecture and relates to a π-version of Alperin's weight conjecture previously established by the authors.
KW - Alternating sums
KW - Dade's conjecture
KW - π-subgroups
UR - http://www.scopus.com/inward/record.url?scp=85137642180&partnerID=8YFLogxK
U2 - 10.1016/j.jpaa.2022.107227
DO - 10.1016/j.jpaa.2022.107227
M3 - Article
AN - SCOPUS:85137642180
VL - 227
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
IS - 3
M1 - 107227
ER -