On the Existence of $f$-local Subgroups in a Group with Finite Involution
| Autor: | A.I. Sozutov, M. V. Yanchenko |
|---|---|
| Jazyk: | English<br />Russian |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Известия Иркутского государственного университета: Серия "Математика", Vol 40, Iss 1, Pp 112-117 (2022) |
| Druh dokumentu: | article |
| ISSN: | 1997-7670 2541-8785 |
| DOI: | 10.26516/1997-7670.2022.40.112 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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