Generalized group identities of subnormal subgroups of general linear groups

Abstract

Let $D$ be a division ring with infinite center, $n$ be a positive integer and $w(x_1,x_2,\cdots ,x_m)=1$ be a generalized group identity over the general linear group $\GL_n(D)$. The aim of this paper is to prove that every subnormal subgroup of $G{L}_n(D)$ which satisfies the generalized group identity $w(x_1,x_2,\cdots ,x_m)=1$ is central.

The paper has been withdrawn by the author due to some mistakes in proofs