Subnormal subgroups of almost locally simple artinian algebras with involutions

In this paper, we investigate subnormal subgroups of the multiplicative group of an almost locally simple artinian algebra with involution. In particular, we show that if either the set of traces or the set of norms of such a subgroup with respect to this involution is central, then the algebra must be either a quaternion division algebra or the matrix ring of degree $2$ over a field.