Resumen de Locally solvable and solvable-by-finite maximal subgroups of GLn(D)

Huynh Viet Khanh, Bui Xuan Hai

• This paper aims to study solvable-by-finite and locally solvable maximal subgroups of an almost subnormal subgroup of the general skew linear group GLn(D) over a division ring D. It turns out that in the case where D is non-commutative, if such maximal subgroups exist, then either it is abelian or [D : F] < ∞. Also, if F is an infinite field and n ≥ 5, then every locally solvable maximal subgroup of a normal subgroup of GLn(F) is abelian.