Zeros of characters and the Frattini subgroup (Q923125)
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scientific article; zbMATH DE number 4168927
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Zeros of characters and the Frattini subgroup |
scientific article; zbMATH DE number 4168927 |
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Zeros of characters and the Frattini subgroup (English)
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1990
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The author proves the following theorem: Let G be a finite group with \(1<Z(G)<G\), Z(G) the center of G, and assume G has an irreducible non- linear character \(\chi\) such that A(\(\chi\)) contains fewer than \(| Z(G)|\) conjugate classes of elements where \(A(\chi)=\{g\in G|\chi (g)=0\}\). Then the Frattini subgroup \(\Phi\) (G)\(\neq 1\).
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finite group
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center
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irreducible non-linear character
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Frattini subgroup
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0.9355094
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0.9194541
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0.9175862
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0.9118955
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0.9066176
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