幂零群的一些判别条件

Some Necessary and Sufficient Conditions for a Nilpotent Group

若群G有一个幂零的正规子群H使得商群G/H幂零,并不能推出G幂零.但对正规子群加强条件由商群的幂零性可以得出原群的幂零性,主要讨论了一些特殊的正规子群构成的商群,比如Z(G),φ(G)等.

We know that if the group G is a nilpotent normal subgroups H of the quotient group G/H is nilpotent, and can not launch G is nilpotent. This paper is mainly discussed on strengthening conditions made by business nilpotency of finite groups which can be drawn from the original nilpotency of finite groups, and mainlyresearched some quotient group which consisting of special normal subgroup, such as Z （G）,φ（G）