Finitely solvable groups with nilpotent wide subgroups
A subgroup $H$ of a finite group $G$ is called wide if each prime divisor of the order of $G$ divides the order of $H$. We obtain a description of finite solvable groups without wide subgroups. It is shown that a finite solvable group with nilpotent wide subgroups contains a quotient group with resp...
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| Date: | 2016 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2016
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1893 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | A subgroup $H$ of a finite group $G$ is called wide if each prime divisor of the order of $G$ divides the order of $H$. We obtain
a description of finite solvable groups without wide subgroups. It is shown that a finite solvable group with nilpotent wide subgroups contains a quotient group with respect to the hypercenter without wide subgroups. |
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