Finite groups with many metacyclic subgroups. (Q2807114)
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scientific article; zbMATH DE number 6582876
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite groups with many metacyclic subgroups. |
scientific article; zbMATH DE number 6582876 |
Statements
19 May 2016
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finite groups
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non-nilpotent groups
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modular groups
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metacyclic groups
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Carter subgroups
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\(2\)-generator subgroups
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0.93343276
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0.93011004
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0.9270536
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0.9240128
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0.92207414
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0.92082185
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Finite groups with many metacyclic subgroups. (English)
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In this paper the authors describe in full detail the structure of finite non-nilpotent groups in which every \(2\)-generator subgroup is metacyclic. In particular, such groups are supersoluble, metabelian and of the form \(G=NC\) with \(N\) a normal abelian subgroup, \(C\) a Carter subgroup of \(G\) and \(N\cap C=1\), moreover every element of \(C\) acts on \(N\) as a power automorphism.
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