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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the supercenter of a group over domains of characteristic 0


Author: Héctor A. Merklen
Journal: Proc. Amer. Math. Soc. 83 (1981), 16-18
MSC: Primary 16A27
MathSciNet review: 619971
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0619971-1
PII: S 0002-9939(1981)0619971-1
Article copyright: © Copyright 1981 American Mathematical Society