On a product of two formational \(\mathrm{tcc}\)-subgroups
A subgroup \(A\) of a group \(G\) is called \(\mathrm{tcc}\)-subgroup in \(G\), if there is a subgroup \(T\) of \(G\) such that \(G=AT\) and for any \(X\le A\) and \(Y\le T\) there exists an element \(u\in \langle X,Y\rangle \) such that \(XY^u\leq G\). The notation \(H\le G \) means that \(H\) is...
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| Дата: | 2021 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2021
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1396 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | A subgroup \(A\) of a group \(G\) is called \(\mathrm{tcc}\)-subgroup in \(G\), if there is a subgroup \(T\) of \(G\) such that \(G=AT\) and for any \(X\le A\) and \(Y\le T\) there exists an element \(u\in \langle X,Y\rangle \) such that \(XY^u\leq G\). The notation \(H\le G \) means that \(H\) is a subgroup of a group \(G\). In this paper we consider a group \(G=AB\) such that \(A\) and \(B\) are \(\mathrm{tcc}\)-subgroups in \(G\). We prove that \(G\) belongs to \(\frak F\), when \(A\) and \(B\) belong to \(\mathfrak{F}\) and \(\mathfrak{F}\) is a saturated formation of soluble groups such that \(\mathfrak{U} \subseteq \mathfrak{F}\). Here \(\mathfrak{U}\) is the formation of all supersoluble groups. |
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