有限群的Fuzzy次正规子群与Fuzzy极大子群

本文研究了有限群的Ｆ次正规子群，得出了一个Ｆ子群是Ｆ次正规子群的充要条件，讨论了Ｆ次正规子群的一些重要性质。另外，本文还引入了有限群的Ｆ极大子群的概念，给出了Ｆ子群是Ｆ极大群的充要条件。最后，给出了三个定理，讨论了有限群Ｇ可解、超可解、幂零与Ｇ的Ｆ次正规子群、Ｆ极大子群之间的联系。

The Fuzzy Subnormal Subgroups and Fuzzy Maximum Subgroups of Finite Groups

In this paper, We study the fuzzy subnormal subgroup of a finite group G. The concept of the fuzzy maximum subgroup of a finite group G is described. The sufficient andnecessary condition is given to prove that a fuzzy subgroup p is a fuzzy subnormal (maximum ) subgroup. Some of interesting consequences of the fuzzy subnormal subgroup arealso given. In addition, We study the relationship between the soluble (supersoluble,nilpotent) group G and the fuzzy subnormal (maximum) subgroup of G and give threetheorems.