Degrees, class sizes and divisors of character values

@article{Gallagher2012DegreesCS,
  title={Degrees, class sizes and divisors of character values},
  author={Patrick X. Gallagher},
  journal={Journal of Group Theory},
  year={2012},
  volume={15},
  pages={455 - 467}
}
  • P. Gallagher
  • Published 1 July 2012
  • Mathematics
  • Journal of Group Theory
Abstract. In the character table of a finite group there is a tendency either for the character degree to divide the conjugacy class size or the character value to vanish. There is also a partial divisibility where the determinant of the character is not 1. There are versions of these depending on a subgroup, based on an arithmetic property of spherical functions which generalizes the integrality of the values of the characters and the central characters. 

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