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Related searches:
Brauer characters and rationality
Mathematische Zeitschrift, 2013Let \(G\) be a finite group and let \(p\) be a prime. In this paper, it is proved that \(G\) has a non-trivial rational valued irreducible \(p\)-Brauer character if and only if \(G\) has a non-trivial rational element of order prime to \(p\). The proof relies on the classification of the finite simple groups.
Gabriel Navarro +2 more
exaly +2 more sources
It is known that a finite group has even order if and only if it has an irreducible character that is rational valued. In this paper, it is shown that the same is true when ordinary characters are replaced by \(p\)-Brauer characters for \(p\) an odd prime (the result fails for \(p=2\)). A stronger result is proved for \(G\) solvable.
Gabriel Navarro +2 more
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Doctor Foundation of Henan University of Technology [2010BS048]; Tian Yuan Foundations [11126273, 11126271]
Wang Huiqun, Chen Xiaoyou, Zeng Jiwen
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