Nilpotent maximal subgroups of GLn(D)

Abstract

AbstractIn [S. Akbari, J. Algebra 217 (1999) 422–433] it has been conjectured that if D is a noncommutative division ring, then D∗ contains no nilpotent maximal subgroup. In connection with this conjecture we show that if GLn(D) contains a nilpotent maximal subgroup, say M, then M is abelian, provided D is infinite. This extends one of the main results appeared in [S. Akbari, J. Algebra 259 (2003) 201–225, Theorem 4]