On the Existence of $f$-local Subgroups in a Group with Finite Involution
An $f$-local subgroup of an infinite group is each its infinite subgroup with a nontrivial locally finite radical. An involution is said to be finite in a group if it generates a finite subgroup with each conjugate involution. An involution is called isolated if it does not commute with any conjugat...
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| Format: | Article |
| Language: | English |
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Irkutsk State University
2022-06-01
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| Series: | Известия Иркутского государственного университета: Серия "Математика" |
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| Online Access: | https://mathizv.isu.ru/en/article/file?id=1415 |
| _version_ | 1811243394108751872 |
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| author | A.I. Sozutov M. V. Yanchenko |
| author_facet | A.I. Sozutov M. V. Yanchenko |
| author_sort | A.I. Sozutov |
| collection | DOAJ |
| description | An $f$-local subgroup of an infinite group is each its infinite subgroup with a nontrivial locally finite radical. An involution is said to be finite in a group if it generates a finite subgroup with each conjugate involution. An involution is called isolated if it does not commute with any conjugate involution. We study the group $G$ with a finite non-isolated involution $i$, which includes infinitely many elements of finite order. It is proved that $G$ has an $f$-local subgroup containing with $i$ infinitely many elements of finite order. The proof essentially uses the notion of a commuting graph. |
| first_indexed | 2024-04-12T14:06:37Z |
| format | Article |
| id | doaj.art-a7606bdd7e3045d49e9df94846ca5c65 |
| institution | Directory Open Access Journal |
| issn | 1997-7670 2541-8785 |
| language | English |
| last_indexed | 2024-04-12T14:06:37Z |
| publishDate | 2022-06-01 |
| publisher | Irkutsk State University |
| record_format | Article |
| series | Известия Иркутского государственного университета: Серия "Математика" |
| spelling | doaj.art-a7606bdd7e3045d49e9df94846ca5c652022-12-22T03:30:03ZengIrkutsk State UniversityИзвестия Иркутского государственного университета: Серия "Математика"1997-76702541-87852022-06-01401112117https://doi.org/10.26516/1997-7670.2022.40.112On the Existence of $f$-local Subgroups in a Group with Finite InvolutionA.I. SozutovM. V. YanchenkoAn $f$-local subgroup of an infinite group is each its infinite subgroup with a nontrivial locally finite radical. An involution is said to be finite in a group if it generates a finite subgroup with each conjugate involution. An involution is called isolated if it does not commute with any conjugate involution. We study the group $G$ with a finite non-isolated involution $i$, which includes infinitely many elements of finite order. It is proved that $G$ has an $f$-local subgroup containing with $i$ infinitely many elements of finite order. The proof essentially uses the notion of a commuting graph.https://mathizv.isu.ru/en/article/file?id=1415group$f$-local subgroupfinite involutioncommuting graph |
| spellingShingle | A.I. Sozutov M. V. Yanchenko On the Existence of $f$-local Subgroups in a Group with Finite Involution Известия Иркутского государственного университета: Серия "Математика" group $f$-local subgroup finite involution commuting graph |
| title | On the Existence of $f$-local Subgroups in a Group with Finite Involution |
| title_full | On the Existence of $f$-local Subgroups in a Group with Finite Involution |
| title_fullStr | On the Existence of $f$-local Subgroups in a Group with Finite Involution |
| title_full_unstemmed | On the Existence of $f$-local Subgroups in a Group with Finite Involution |
| title_short | On the Existence of $f$-local Subgroups in a Group with Finite Involution |
| title_sort | on the existence of f local subgroups in a group with finite involution |
| topic | group $f$-local subgroup finite involution commuting graph |
| url | https://mathizv.isu.ru/en/article/file?id=1415 |
| work_keys_str_mv | AT aisozutov ontheexistenceofflocalsubgroupsinagroupwithfiniteinvolution AT mvyanchenko ontheexistenceofflocalsubgroupsinagroupwithfiniteinvolution |