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Abstract
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Given a non-commutative finite dimensional F-central division algebra D, we
study conditions under which every non-abelian maximal subgroup M of GLn(D) contains
a non-cyclic free subgroup. In general, it is shown that either M contains a non-cyclic free
subgroup or there exists a unique maximal sub¯eld K of Mn(D) such that N_GLn(D)(K^*)=M) M, K¤ CM, K=F is Galois with Gal(K=F»=
M=K¤, and F[M] = Mn(D). In particular,
when F is global or local, it is proved that if ([D : F]; Char(F)) = 1, then every non-
abelian maximal subgroup of GL1(D) contains a non-cyclic free subgroup. Furthermore,
it is also shown that GLn(F) contains no solvable maximal subgroups provided that F is
local or global and n ¸ 5.
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