Restriction of characters to Sylow normalizers (Q2731123)
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scientific article; zbMATH DE number 1625569
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Restriction of characters to Sylow normalizers |
scientific article; zbMATH DE number 1625569 |
Statements
Restriction of characters to Sylow normalizers (English)
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3 February 2002
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\(p\)-solvable groups
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irreducible characters
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Sylow normalizers
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Sylow subgroups
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Let \(G\) be a finite group, \(P\) a Sylow \(p\)-subgroup of \(G\) and \(N_G(P)\) its normalizer. The main result of the paper states that if \(G\) is \(p\)-solvable and \(\chi\) is an irreducible character of \(G\) of \(p'\)-degree, then the restriction of \(\chi\) to \(N_G(P)\) is irreducible if and only if \(G=\ker(\chi)N_G(P)\). Examples are given to show that the assumption on the degree of \(\chi\) cannot be removed.
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