On the Hughes problem for exponent \(p^ 2\) (Q790245)
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scientific article; zbMATH DE number 3847652
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Hughes problem for exponent \(p^ 2\) |
scientific article; zbMATH DE number 3847652 |
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On the Hughes problem for exponent \(p^ 2\) (English)
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1984
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If G is a finite group and p a prime, define \(H_{p^ 2}(G)=<x\in G| \quad x^{p^ 2}\neq 1>.\) Assuming that G is not a p-group, p is odd and a Sylow p-subgroup of G is metabelian, it is shown that \(| G:H_{p^ 2}(G)| \leq p^ p.\) The bound is best possible.
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Hughes problem
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metabelian Sylow p-subgroup
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0.8533451
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0.8524424
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0.8520579
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0.8518213
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