SOLUBLE MAXIMAL SUBGROUPS IN GLn(D)

Let D be an F-central non-commutative division ring. Here, it is proved that if GL(n)(D) contains a non-abelian soluble maximal subgroup, then n = 1, [D : F] < infinity, and D is cyclic of degree p, a prime. Furthermore, a classification of soluble maximal subgroups of GL(n)(F) for an algebraically closed or real closed field F is also presented. We then determine all soluble maximal subgroups of GL(2)(F) for fields F with Char F not equal 2.