Abstract
The principal $p$-block of a finite group $G$ contains only one real-valued irreducible ordinary character exactly when $G/{{\bf O}-{p'}(G)}$ has odd order. For $p \ne 3$, the same happens with rational-valued characters. We also prove an analogue for $p$-Brauer characters with $p \geq 3$.
Original language | English (US) |
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Pages (from-to) | 1955-1973 |
Number of pages | 19 |
Journal | International Mathematics Research Notices |
Volume | 2019 |
Issue number | 7 |
DOIs | |
State | Published - Apr 1 2019 |
Keywords
- 20C15
- 20C20
ASJC Scopus subject areas
- Mathematics(all)