In a paper titled "Trivial units in Group Rings" by Farkas, what does it mean by Finite conjugate subgroup. Here is the related image attached-
What is finite conjugate subgroup of a group? It is not clear to me what is author referring here.
2026-03-25 19:00:41.1774465241
Finite conjugate subgroup
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I had never heard of this before, but after a bit of searching, I found the definition $\Delta(G) = \{ g \in G : |G:C_G(g)| < \infty \}$ or, in other words, the elements of $G$ whose conjugacy classes in $G$ are finite. It is easy to see that $\Delta(G)$ is a normal (in fact characteristic) subgroup of $G$. Apparently it arises frequently in the study of group rings, and one source cited Passman's book on Infinite group Rings as a source for its basic properties.