Abstract. Let $R[G]$ be the group ring of a group $G$ over an associative ring $R$ with unity such that all prime divisors of orders of elements of $G$ are invertible in $R$. If $R$ is finite and $G$ is a Chernikov (torsion $FC$-) group, then each $R$-derivation of $R[G]$ is inner. Similar results also are obtained for other classes of groups $G$ and rings $R$.
AMS Subject Classification
(1991): 20C05, 16S34, 20F45, 20F19, 16W25
locally finite group,
differentially trivial ring,
nilpotent Lie ring,
solvable Lie ring
received 18.6.2019, revised 19.2.2020, accepted 20.2.2020. (Registered under 664/2019.)