Bounds on orders of finite subgroups of \(\text{PGL}_n(K)\)
Let \(B(K,n)\) and \(B'(K,n)\) denote the statements that there is a bound on the orders of the finite nonmodular subgroups of \(\text{GL}_n(K)\) and \(\text{PGL}_n(K)\), respectively. The authors show that \(B(K,n)\) is equivalent to \(B'(K,n)\) for all \(n\geq 2\). They also characterize \(B(K,n)\) in terms of cyclotomic extensions of \(K\) and they apply their results to the multiplicative subgroups of finite dimensional central simple \(K\)-algebras.
scientific article; zbMATH DE number 1247582