A characterization of finite projective special unitary groups \(U_4(q)\) and \(U_5(q)\) (Q2774185)
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scientific article; zbMATH DE number 1713446
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A characterization of finite projective special unitary groups \(U_4(q)\) and \(U_5(q)\) |
scientific article; zbMATH DE number 1713446 |
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8 August 2002
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unitary groups
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Sylow subgroups
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normalizers
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A characterization of finite projective special unitary groups \(U_4(q)\) and \(U_5(q)\) (English)
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Let \(G\) be a finite group. The author proves that \(G\simeq U_n(q)\), \(n=4\) or \(5\), if and only if the normalizers of their Sylow \(p\)-subgroups have the same order for every prime \(p\), \(p\in\pi(G)\). This is a consequence of the following result: \(G\simeq U_n(q)\), \(n=3\), if and only if the normalizers of their Sylow \(p\)-subgroups have the same order for every prime \(p\), \(p\in\pi(G)\) [A new characterization of the finite projective special unitary group \(U_3(q)\), J. Liaoning Univ., Nat. Sci. 23, No. 4, 1-4 (1996)].
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