The structure of groups with cyclic commutator subgroups indecomposable to a subdirect product of groups
| Autor: | Kozlov, Vladimir Anatolievich, Titov, Georgiy Nikolaevich |
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| Jazyk: | English<br />Russian |
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика, Vol 21, Iss 4, Pp 442-447 (2021) |
| Druh dokumentu: | article |
| ISSN: | 1816-9791 2541-9005 |
| DOI: | 10.18500/1816-9791-2021-21-4-442-447 |
| Popis: | The article studies finite groups indecomposable to subdirect product of groups (subdirectly irreducible groups), commutator subgroups of which are cyclic subgroups. The article proves that extensions of a primary cyclic group by any subgroup of its automorphisms completely describe the structure of non-primary finite subdirectly irreducible groups with a cyclic commutator subgroup. The following theorem is the main result of this article: a finite non-primary group is subdirectly irreducible with a cyclic commutator subgroup if and only if for some prime number $p\geq 3$ it contains a non-trivial normal cyclic $p$-subgroup that coincides with its centralizer in the group. In addition, it is shown that the requirement of non-primality in the statement of the theorem is essential. |
| Databáze: | Directory of Open Access Journals |
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