ACTA issues

Derivations of group rings

Orest D. Artemovych, Victor A. Bovdi, Mohamed A. Salim

Acta Sci. Math. (Szeged) 86:1-2(2020), 51-72

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 $R$.

DOI: 10.14232/actasm-019-664-x

AMS Subject Classification (1991): 20C05, 16S34, 20F45, 20F19, 16W25

Keyword(s): group ring, derivation, locally finite group, solder, torsion-free group, nilpotent 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.)