On minimal \(\omega\)-composition non-\(\frak H\)-formations
Let \(\frak{H}\) be some class of groups. A formation \(\frak{F}\) is called a minimal \(\tau\)-closed \(\omega\)-composition non-\(\frak{H}\)-formation [1] if \(\frak{F} \nsubseteq \frak{H}\) but \(\frak{F}_1 \subseteq \frak{H}\) for all proper \(\tau\)-closed \(\omega\)-composition subformations \...
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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/903 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | Let \(\frak{H}\) be some class of groups. A formation \(\frak{F}\) is called a minimal \(\tau\)-closed \(\omega\)-composition non-\(\frak{H}\)-formation [1] if \(\frak{F} \nsubseteq \frak{H}\) but \(\frak{F}_1 \subseteq \frak{H}\) for all proper \(\tau\)-closed \(\omega\)-composition subformations \(\frak{F}_1\) of \(\frak{F}\). In this paper we describe the minimal \(\tau\)-closed \(\omega\)-composition non-\(\frak{H}\)-formations, where \(\frak H\) is a \(2\)-multiply local formation and \(\tau\) is a subgroup functor such that for any group \(G\) all subgroups from \(\tau(G)\) are subnormal in \(G\). |
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