Geodesic
On the existence of $f$-local subgroups in a group with finite involution
The Bulletin of Irkutsk State University. Series Mathematics, Tome 40 (2022), pp. 112-117

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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.
Keywords: $f$-local subgroup, finite involution, commuting graph.
Mots-clés : group 
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     title = {On the existence of $f$-local subgroups in a group with finite involution},
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Anatoly I. Sozutov; Mikhail V. Yanchenko. On the existence of $f$-local subgroups in a group with finite involution. The Bulletin of Irkutsk State University. Series Mathematics, Tome 40 (2022), pp. 112-117. http://geodesic.mathdoc.fr/item/IIGUM_2022_40_a8/