Post-classification version of Jordan's theorem on finite linear groups
AUTOR(ES)
Weisfeiler, Boris
RESUMO
Using classification of finite simple groups, I show that a finite subgroup G of GLn(C), where C = the complex numbers, contains a commutative normal subgroup M of index at most (n + 1)!nalogn+b. Moreover, if G is primitive and does not contain normal subgroups that are direct products of large alternating groups, then the factor (n + 1)! can be dropped. I further show that similar statements hold also in characteristics p ≥ 2, if one takes M to be an extension of a group of Lie type of characteristic p by a solvable group that has a normal p-subgroup with commutative p′-quotient. These results improve the celebrated theorems of Jordan and of Brauer and Feit.
