On large subgroups of finite groups (Q1204399)
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scientific article; zbMATH DE number 130487
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On large subgroups of finite groups |
scientific article; zbMATH DE number 130487 |
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On large subgroups of finite groups (English)
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28 March 1993
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If \(G\) is a finite group, not of prime order, then \(G\) has a proper subgroup \(H\) with \(| H| \geq | G|^{1/2}\). Considering the case that the order of \(G\) is \(p^ 2\), \(p\) a prime, this bound is best possible. The proof uses the classification of the finite simple groups.
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finite group
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proper subgroup
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classification of the finite simple groups
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