广义极小非幂零群

Generalized Minimal Non-nilpotent Groups

若有限群非幂零但其所有真子群均幂零,则称其为一个极小非幂零群.一类群称为广义极小非幂零群,如果它有一个非幂零真子群使得其它不包含在这个子群中的所有真子群均为幂零的.证得这类群可解,并讨论了该类群的子群的性质.

If a finite group is not nilpotent but all of its proper subgroups are nilpotent, then call it a minimal non-nilpotent group. In this paper,call a finite group a generalized minimal non-nilpotent group, if it possesses a proper non-nilpotent subgroup such that any other subgroup not contained in this subgroup is nilpotent. The author proves this group is soluble and discusses the properties of its subgroups.