On division subrings normalized by almost subnormal subgroups in division rings

Abstract

Let D be a division ring with infinite center, K a proper division subring of D and N an almost subnormal subgroup of the multiplicative group $$D^*$$ of D. The aim of this paper is to show that if K is N-invariant and N is non-central, then K is central. Some examples of almost subnormal subgroups in division rings that are not subnormal are also given.