Locally Finite Groups Saturated with Direct Product of Two Finite Dihedral Groups
In the study of infinite groups, as a rule, some finiteness conditions are imposed. For example, the group is required to be periodic, Shunkov group, Frobenius group, locally finite group. The concept of saturation makes it possible to effectively establish the internal structure of various classes...
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| Format: | Article |
| Language: | English |
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Irkutsk State University
2023-06-01
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| Series: | Известия Иркутского государственного университета: Серия "Математика" |
| Subjects: | |
| Online Access: | http://mathizv.isu.ru/en/article/file?id=1451 |
| _version_ | 1797810612619706368 |
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| author | A. V. Kukharev A.A. Shlepkin |
| author_facet | A. V. Kukharev A.A. Shlepkin |
| author_sort | A. V. Kukharev |
| collection | DOAJ |
| description | In the study of infinite groups, as a rule, some finiteness conditions are imposed. For example, the group is required to be periodic, Shunkov group, Frobenius group, locally finite group. The concept of saturation makes it possible to effectively establish the internal structure of various classes of infinite groups. To date, a large array of results on groups saturated with various classes of finite groups has been obtained. Another important direction in the study of groups with saturation conditions is the study of groups saturated with direct products of various groups. In this paper, a partial solution to the problem of B. Amberg and L.S. Kazarin on periodic groups saturated with dihedral groups in the class of locally finite groups. The structure of a locally finite group saturated with a direct product of two finite dihedral groups is established and it is proved that in this case the group is solvable. The result obtained is an important step towards solving the problem of Amberg and Kazarin. |
| first_indexed | 2024-03-13T07:10:24Z |
| format | Article |
| id | doaj.art-0965c62964a549fe958b35ef694c1a32 |
| institution | Directory Open Access Journal |
| issn | 1997-7670 2541-8785 |
| language | English |
| last_indexed | 2024-03-13T07:10:24Z |
| publishDate | 2023-06-01 |
| publisher | Irkutsk State University |
| record_format | Article |
| series | Известия Иркутского государственного университета: Серия "Математика" |
| spelling | doaj.art-0965c62964a549fe958b35ef694c1a322023-06-06T03:41:46ZengIrkutsk State UniversityИзвестия Иркутского государственного университета: Серия "Математика"1997-76702541-87852023-06-014417181https://doi.org/10.26516/1997-7670.2023.44.71Locally Finite Groups Saturated with Direct Product of Two Finite Dihedral GroupsA. V. KukharevA.A. ShlepkinIn the study of infinite groups, as a rule, some finiteness conditions are imposed. For example, the group is required to be periodic, Shunkov group, Frobenius group, locally finite group. The concept of saturation makes it possible to effectively establish the internal structure of various classes of infinite groups. To date, a large array of results on groups saturated with various classes of finite groups has been obtained. Another important direction in the study of groups with saturation conditions is the study of groups saturated with direct products of various groups. In this paper, a partial solution to the problem of B. Amberg and L.S. Kazarin on periodic groups saturated with dihedral groups in the class of locally finite groups. The structure of a locally finite group saturated with a direct product of two finite dihedral groups is established and it is proved that in this case the group is solvable. The result obtained is an important step towards solving the problem of Amberg and Kazarin.http://mathizv.isu.ru/en/article/file?id=1451locally finite groupdirect product of groupsdihedral groupsaturation with a given set of groups |
| spellingShingle | A. V. Kukharev A.A. Shlepkin Locally Finite Groups Saturated with Direct Product of Two Finite Dihedral Groups Известия Иркутского государственного университета: Серия "Математика" locally finite group direct product of groups dihedral group saturation with a given set of groups |
| title | Locally Finite Groups Saturated with Direct Product of Two Finite Dihedral Groups |
| title_full | Locally Finite Groups Saturated with Direct Product of Two Finite Dihedral Groups |
| title_fullStr | Locally Finite Groups Saturated with Direct Product of Two Finite Dihedral Groups |
| title_full_unstemmed | Locally Finite Groups Saturated with Direct Product of Two Finite Dihedral Groups |
| title_short | Locally Finite Groups Saturated with Direct Product of Two Finite Dihedral Groups |
| title_sort | locally finite groups saturated with direct product of two finite dihedral groups |
| topic | locally finite group direct product of groups dihedral group saturation with a given set of groups |
| url | http://mathizv.isu.ru/en/article/file?id=1451 |
| work_keys_str_mv | AT avkukharev locallyfinitegroupssaturatedwithdirectproductoftwofinitedihedralgroups AT aashlepkin locallyfinitegroupssaturatedwithdirectproductoftwofinitedihedralgroups |