表特殊线性群中元素为平延换位子之积

摘要

We consider the special linear group SLnF over a field F with more than three elements.Let resA denote rank(A-I) for any A in GLnF.A matrix A is called a transvection if resA＝1 and detA＝1. For n＞2,we prove that every matrix A in SLn F is a productof at most [resA/2]+2 Commutators of transvections.%考虑元素个数大于3的域F上的特殊线性群SLnF.对GLnF中任一矩阵A,记resA为A-I的秩.称矩阵A为平延，如果resA=1并且detA=1.对n＞2，本文证明SLnF中任一矩阵都可写成不超过[resA/2]+2个平延换位子之积.