On Frattini subformations of formations of finite \(n\)-ary groups (Q2736162)
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scientific article; zbMATH DE number 1638291
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Frattini subformations of formations of finite \(n\)-ary groups |
scientific article; zbMATH DE number 1638291 |
Statements
29 August 2001
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\(n\)-ary groups
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formations
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minimal congruences
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maximal subformations
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On Frattini subformations of formations of finite \(n\)-ary groups (English)
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A class \(\Phi\) of \(n\)-ary groups is called a formation if: (i) for every \(n\)-ary group \(G\in\Phi\) and every congruence \(\pi\), \(G/\pi\in\Phi\), (ii) \(H/\pi_1\in\Phi\) and \(H/\pi_2\in\Phi\) imply \(H/\pi_1\cap\pi_2\in\Phi\).NEWLINENEWLINENEWLINEDenote by \(\text{soc}(G)\) the product of all minimal congruences of \(G\). The author proves that \(G/\text{soc}(G)\) belongs to every maximal subformation of \(\Phi\).
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0.8198270201683044
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