矩阵环的有限乘法子群

Finite Multiplicative Subgroups in Matrix Rings

将Minkowski关于有限整数矩阵群的著名结果推广到一般的环上,主要结果是证明了:对任意环R,如果R的加法群为有限生成的自由Abel群,则R的所有乘法可逆元构成的群U(R)中的有限子群精确到同构只有有限多个.

This paper generalizes the famous result of finite groups of integer matrices due to Minkowski to general rings.It is proved that for an arbitrary ring R,if its additive group is finitely generalized free Abelian group,then the multiplicative group U（R） only contains finitely many finite subgroups up to isomorphism.