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Abstract
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Let D be an F-central non-commutative division ring. Here, it is proved that if GLn(D)
contains a non-abelian soluble maximal subgroup, then n = 1, [D : F] < ∞, and D is
cyclic of degree p, a prime. Furthermore, a classification of soluble maximal subgroups
of GLn(F) for an algebraically closed or real closed field F is also presented. We then
determine all soluble maximal subgroups of GL2(F) for fields F with Char F = 2.
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