Details
| Original language | English |
|---|---|
| Pages (from-to) | 296-311 |
| Number of pages | 16 |
| Journal | Journal of algebra |
| Volume | 560 |
| Early online date | 26 May 2020 |
| Publication status | Published - 15 Oct 2020 |
Abstract
Let G be a finite group, p a prime, and IBrp(G) the set of irreducible p-Brauer characters of G. Let e¯p(G) be the largest integer such that pe¯p(G) divides χ(1) for some χ∈IBrp(G). We show that |G:Op(G)|p≤pke¯p(G) for an explicitly given constant k. We also study the analogous problem for the p-parts of the conjugacy class sizes of p-regular elements of finite groups.
Keywords
- Brauer characters, p-parts, p-regular classes
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Journal of algebra, Vol. 560, 15.10.2020, p. 296-311.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On p-parts of Brauer character degrees and p-regular conjugacy class sizes of finite groups
AU - Bessenrodt, Christine
AU - Yang, Yong
N1 - Funding Information: This work was partially supported by the NSFC (No. 11671063 ), and a grant from the Simons Foundation (No. 499532, YY ). We would also like to thank the referee for the valuable suggestions.
PY - 2020/10/15
Y1 - 2020/10/15
N2 - Let G be a finite group, p a prime, and IBrp(G) the set of irreducible p-Brauer characters of G. Let e¯p(G) be the largest integer such that pe¯p(G) divides χ(1) for some χ∈IBrp(G). We show that |G:Op(G)|p≤pke¯p(G) for an explicitly given constant k. We also study the analogous problem for the p-parts of the conjugacy class sizes of p-regular elements of finite groups.
AB - Let G be a finite group, p a prime, and IBrp(G) the set of irreducible p-Brauer characters of G. Let e¯p(G) be the largest integer such that pe¯p(G) divides χ(1) for some χ∈IBrp(G). We show that |G:Op(G)|p≤pke¯p(G) for an explicitly given constant k. We also study the analogous problem for the p-parts of the conjugacy class sizes of p-regular elements of finite groups.
KW - Brauer characters
KW - p-parts
KW - p-regular classes
UR - http://www.scopus.com/inward/record.url?scp=85085645311&partnerID=8YFLogxK
U2 - 10.1016/j.jalgebra.2020.05.018
DO - 10.1016/j.jalgebra.2020.05.018
M3 - Article
AN - SCOPUS:85085645311
VL - 560
SP - 296
EP - 311
JO - Journal of algebra
JF - Journal of algebra
SN - 0021-8693
ER -