Normal subgroups of the multiplicative group of a ring

In the paper we study the construction of $K$-linearly independent normal subgroups of the multiplicative group $U(R)$ of an algebra $R$ over a ring $K$ of characteristic $p^m$ and their ordering inside the groups $U(R)$. We also describe the group rings whose multiplicative group contains a $K$-linearly independent normal subgroup not belonging to the center and containing an element of finite order. We also study abelian normal subgroups of the multiplicative group of the ring of a $p$-group over a ring of characteristic $p$.
Bibliography: 10 titles.