### Abstract

We prove that, for any generalized character ¿, other than a multiple of the regular character, of any finite group G, we have

Sg¿G# |¿(g)|2 = |G|/x(1) - 1,

where ¿ is an irreducible character of maximal degree of G and G# is the set of non-identity elements of G. We also determine exactly when equality is achieved.

Sg¿G# |¿(g)|2 = |G|/x(1) - 1,

where ¿ is an irreducible character of maximal degree of G and G# is the set of non-identity elements of G. We also determine exactly when equality is achieved.

Original language | English |
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Pages (from-to) | 323-328 |

Number of pages | 6 |

Journal | Bulletin of the London Mathematical Society |

Volume | 42 |

Issue number | 2 |

Early online date | 19 Feb 2010 |

DOIs | |

Publication status | Published - Apr 2010 |