Factorization of periodic locally solvable groups by locally nilpotent and nilpotent subgroups (Q2784889)
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scientific article; zbMATH DE number 1733120
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Factorization of periodic locally solvable groups by locally nilpotent and nilpotent subgroups |
scientific article; zbMATH DE number 1733120 |
Statements
24 April 2002
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locally solvable groups
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products of groups
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locally nilpotent subgroups
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Fitting subgroups
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derived lengths
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Factorization of periodic locally solvable groups by locally nilpotent and nilpotent subgroups (English)
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The paper continues a series of four papers of the author [see Ukr. Mat. Zh. 53, No. 4, 531-541 (2001; Zbl 0992.20016), ibid. 52, No. 6, 809-819 (2000; Zbl 0956.20012), ibid. 52, No. 7, 965-970 (2000; Zbl 0956.20038), Vopr. Algebry 11, 90-115 (1997; Zbl 0912.20023)] which deal with products of two groups. The main results of the present paper are theorems A-E. The first theorem gives some properties of a finite solvable group \(G=AB\) by passing to the factor group by its Fitting or Frattini subgroup in connection with properties of the subgroups \(A\) and \(B\). In theorems B, C, and E a periodic locally solvable group \(G\) is studied which is the product \(G=AB\) of locally nilpotent subgroups \(A\) and \(B\). Under various restrictions on the group \(G\) and its subgroups \(A\) and \(B\) the structure of \(G\) is investigated.
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