On certain products of soluble groups (Q2716432)
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scientific article; zbMATH DE number 1598946
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On certain products of soluble groups |
scientific article; zbMATH DE number 1598946 |
Statements
On certain products of soluble groups (English)
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20 May 2001
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products of groups
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soluble groups
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finiteness conditions
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mutually permutable groups
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products of soluble subgroups
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factorized groups
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derived lengths
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The authors consider groups \(G=HK\) which are the product of two soluble subgroups \(H\) and \(K\) and satisfy additional permutability requirements, namely that certain subgroups of \(H\) commute with certain subgroups of \(K\). Under these conditions the structure of the factorized group \(G\) is investigated, and it is shown that certain group theoretical properties (in particular finiteness conditions) are inherited by these products. Also bounds for the derived length of these products are given in some cases.
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