SUBGROUPS OF THE MULTIPLICATIVE GROUP OF THE DIVISION RING OF REAL QUATERNIONS

Abstract

Let  be the division ring of real quaternions and  the multiplicative group of  A subgroup  of  is said to be almost subnormal if a sequence of subgroups exists

such that for any    is normal in  or  has the finite index in  In this paper, we show that every almost subnormal subgroup of  is normal.