On the supercenter of a group over domains of characteristic 0

Merklen, Héctor A.

doi:10.1090/S0002-9939-1981-0619971-1

On the supercenter of a group over domains of characteristic $0$
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by Héctor A. Merklen PDF

Proc. Amer. Math. Soc. 83 (1981), 16-18 Request permission

Abstract:

Let $G$ be a group and $R$ a commutative ring with 1 and let ${U_R}G$ be the group of units of the group ring $RG$. The $R$-supercenter of $G$, ${S_R}G$ is the set of elements of $G$ which have a finite number of conjugates under ${U_R}G$. The super-center is studied in the case where $R$ is a domain of characteristic 0. It is shown that for the most important cases the supercenter coincides with the center of the group and with the intersection of all group bases of the group ring.

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