有限N^N-群中的非正规子群

Non-normal Subgroups in finite N^N-groups

有限NN-群指的是每个子群的幂零剩余都正规的有限群.利用非正规子群的共轭类类数,给出了判断一个非幂零群是否为NN-群的充分条件,并且这个非正规子群的共轭类类数的界是最佳的.

A finite group is called NN-group if the nilpotent residual of every subgroup is normal.Using the number of conjugate classes of non-normal subgroups,a sufficient conditions are given for judging that a non-nilpotent group can be a NN-group,and the number of conjugate classes of non-normal subgroups is optimal upper bound.