On the generalized norm of a finite group. (Q2788753)
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scientific article; zbMATH DE number 6543469
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the generalized norm of a finite group. |
scientific article; zbMATH DE number 6543469 |
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22 February 2016
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finite groups
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characteristic subgroups
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generalized norm
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soluble groups
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subnormal subgroups
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intersections of normalizers
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derived subgroup
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0.9644721
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0.9467588
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On the generalized norm of a finite group. (English)
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Let \(G\) be a finite group. The aim of this paper is to investigate two characteristic subgroups \(\omega^{\mathcal A}(G)\) and \(\theta^{\mathcal A}(G)\) of \(G\), which are defined as the intersections of the normalizers of derived subgroups of subnormal and non-subnormal subgroups of \(G\), respectively. Some nice results are proved, e.g. (Theorem 3.3): \(C_G(G')=1\) if and only if \(\theta^{\mathcal A}(G)=1\).
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