Large cyclic subgroups contain non-trivial normal subgroups (Q2747314)
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scientific article; zbMATH DE number 1657498
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Large cyclic subgroups contain non-trivial normal subgroups |
scientific article; zbMATH DE number 1657498 |
Statements
Large cyclic subgroups contain non-trivial normal subgroups (English)
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4 September 2002
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characteristic subgroups
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Fitting groups
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regular orbits
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normal subgroups
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cyclic subgroups
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orders of elements
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automorphisms
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The following result is proved: Let \(G\neq 1\) be a finite group, with a cyclic subgroup \(A\) such that \(|A|>|G|^{1/2}\) [\(|A|\geq|G|^{1/2}\)]. Then \(A\) contains a non-trivial characteristic [normal] subgroup \(B\). Furthermore, some corollaries are derived concerning the maximal order of elements, of automorphisms etc.
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