关于任意子群在其正规闭包指数有界的群性质

On the property of groups with bounded index of every subgroup in its normal closure

文章主要研究了任意子群在其正规闭包指数有界的群性质.首先在局部幂零条件下研究S*-群,得到了它们的幂零类不超过3;然后在有限生成条件下研究一般的S*-群,得到了它们是多重循环群.

In this paper,the author studies the property of groups with bounded index of every subgroup in its normal closure.The author gets the nilpotent class of locally nilpotent S＊-group G is at most 3 and finitely generated S＊-group G is polycyclic group.