Locally solvable maximal subgroups in division rings

Abstract

Let D be a division ring with center F, and let G be an almost subnormal subgroup of $D^{\ast }$. In this paper, we show that if G contains a non-abelian locally solvable maximal subgroup, then D must be a cyclic algebra of prime degree over F. Moreover, it is proved that every locally nilpotent maximal subgroup of G is abelian.