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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| Datum: | 2021 |
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Lugansk National Taras Shevchenko University
2021
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admjournalluguniveduua-article-13962021-01-29T09:38:49Z On a product of two formational \(\mathrm{tcc}\)-subgroups Trofimuk, A. supersoluble group, totally permutable product, saturated formation, tcc-permutable product, tcc-subgroup 20D10 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. Lugansk National Taras Shevchenko University 2021-01-29 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1396 10.12958/adm1396 Algebra and Discrete Mathematics; Vol 30, No 2 (2020) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1396/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1396/535 Copyright (c) 2021 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2021-01-29T09:38:49Z |
| collection |
OJS |
| language |
English |
| topic |
supersoluble group totally permutable product saturated formation tcc-permutable product tcc-subgroup 20D10 |
| spellingShingle |
supersoluble group totally permutable product saturated formation tcc-permutable product tcc-subgroup 20D10 Trofimuk, A. On a product of two formational \(\mathrm{tcc}\)-subgroups |
| topic_facet |
supersoluble group totally permutable product saturated formation tcc-permutable product tcc-subgroup 20D10 |
| format |
Article |
| author |
Trofimuk, A. |
| author_facet |
Trofimuk, A. |
| author_sort |
Trofimuk, A. |
| title |
On a product of two formational \(\mathrm{tcc}\)-subgroups |
| title_short |
On a product of two formational \(\mathrm{tcc}\)-subgroups |
| title_full |
On a product of two formational \(\mathrm{tcc}\)-subgroups |
| title_fullStr |
On a product of two formational \(\mathrm{tcc}\)-subgroups |
| title_full_unstemmed |
On a product of two formational \(\mathrm{tcc}\)-subgroups |
| title_sort |
on a product of two formational \(\mathrm{tcc}\)-subgroups |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2021 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1396 |
| work_keys_str_mv |
AT trofimuka onaproductoftwoformationalmathrmtccsubgroups |
| first_indexed |
2025-12-02T15:34:47Z |
| last_indexed |
2025-12-02T15:34:47Z |
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1850411254435282944 |