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 |