An identification theorem for the locally finite nontwisted Chevalley groups
In this paper, a Chevalley group means a nontwisted Chevalley group. The main result of this paper is: Theorem. Let \(G=\cup_{i\in \omega}G_ i\) where each \(G_ i\) is isomorphic to a Chevalley group of type \({\mathcal L}\) over a finite field. Then G is isomorphic to a Chevalley group of type \({\mathcal L}\) over a locally finite field. Let \(\Phi\) denote a root system for Chevalley groups of type \({\mathcal L}\). The proof of this result uses: a result of Bryant to construct root subgroups \(X_ r\) for each \(r\in \Phi\), a result of Kegel to identify the subgroups \(<X_ r,X_{-r}>\) for each \(r\in \Phi\) and a theorem of Steinberg to identify G.
scientific article; zbMATH DE number 3849479