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RESEARCH PRODUCT

On Real and Rational Characters in Blocks

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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 $p \geq 3$.