Sharp characters of finite groups

Peter J. Cameron; Masao Kiyota

doi:10.1016/0021-8693(88)90285-2

Sharp characters of finite groups

Peter J. Cameron^*, Masao Kiyota

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

If χ is a virtual (generalized) character of a finite group G, with n=χ and L={χ(g)|g∈G, g≠1 {χ(g)|gε{lunate}G, g ≠ 1}, then |G| dividesf_L(n), where f_L(x) is the monic polynomial of least degree having L as its set of roots. (This generalises a result of the second author for permutation characters.) We say that the pair ((G,χ)) is L-sharp if |G|=f_L(n). We characterise the L-sharp pairs for various sets L, sometimes under additional hypotheses, and give a number of examples.

Original language	English
Pages (from-to)	125-143
Number of pages	19
Journal	Journal of Algebra
Volume	115
Issue number	1
DOIs	https://doi.org/10.1016/0021-8693(88)90285-2
Publication status	Published - 15 May 1988

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abstract = "If χ is a virtual (generalized) character of a finite group G, with n=χ and L={χ(g)|g∈G, g≠1 {χ(g)|gε{lunate}G, g ≠ 1}, then |G| dividesfL(n), where fL(x) is the monic polynomial of least degree having L as its set of roots. (This generalises a result of the second author for permutation characters.) We say that the pair ((G,χ)) is L-sharp if |G|=fL(n). We characterise the L-sharp pairs for various sets L, sometimes under additional hypotheses, and give a number of examples.",

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AB - If χ is a virtual (generalized) character of a finite group G, with n=χ and L={χ(g)|g∈G, g≠1 {χ(g)|gε{lunate}G, g ≠ 1}, then |G| dividesfL(n), where fL(x) is the monic polynomial of least degree having L as its set of roots. (This generalises a result of the second author for permutation characters.) We say that the pair ((G,χ)) is L-sharp if |G|=fL(n). We characterise the L-sharp pairs for various sets L, sometimes under additional hypotheses, and give a number of examples.

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Sharp characters of finite groups

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