Finite groups in which every irreducible character vanishes on at most two conjugacy classes (Q2716444)
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scientific article; zbMATH DE number 1599005
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite groups in which every irreducible character vanishes on at most two conjugacy classes |
scientific article; zbMATH DE number 1599005 |
Statements
24 February 2002
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finite nonsoluble groups
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irreducible characters
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simple groups
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solvable groups
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Frobenius groups
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Finite groups in which every irreducible character vanishes on at most two conjugacy classes (English)
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Let \(G\) be a non-Abelian finite group in which every irreducible ordinary character vanishes on at most two conjugacy classes. The authors prove that either \(G\) is isomorphic to one of the simple groups \(A_7\), \(L_2(7)\), or \(G\) is solvable and possesses a normal chain of subgroups \(Z<F\leq G\) such that \(|Z|\leq 2\), \(|G/F|\leq 2\) and \(F/Z\) is a Frobenius group with Frobenius complement of order 2 or 3.
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