On the minimal norm of a non-regular generalized character of an arbitrary finite group

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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.
Original languageEnglish
Pages (from-to)323-328
Number of pages6
JournalBulletin of the London Mathematical Society
Volume42
Issue number2
Early online date19 Feb 2010
DOIs
Publication statusPublished - Apr 2010

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Finite Group
Norm
Irreducible Character
Arbitrary
Equality
Character

Cite this

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title = "On the minimal norm of a non-regular generalized character of an arbitrary finite group",
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.",
author = "Geoffrey Robinson",
year = "2010",
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language = "English",
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AU - Robinson, Geoffrey

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AB - 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.

U2 - 10.1112/blms/bdp129

DO - 10.1112/blms/bdp129

M3 - Article

VL - 42

SP - 323

EP - 328

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

SN - 0024-6093

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