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模糊S-拟正规嵌入子群的同态性质研究
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Abstract:
本文在模糊S-拟正规子群的基础上提出了模糊S-拟正规嵌入子群的概念，利用既约集合套理论对模糊S-拟正规嵌入子群进行了研究。首先给出了群的模糊子群是模糊S-拟正规嵌入的当且仅当它的水平子集是通常群论意义上的S-拟正规嵌入，其次讨论了模糊S-拟正规嵌入子群的同态性质，最后将同态性质推广到了模糊S-拟正规子群。
In the paper, based on the fuzzy S-quasinormal subgroups, the concept of fuzzy S-quasinormally embedded subgroups is proposed and studied by using irreducible nested sets. Firstly, it is given that a fuzzy subgroup of a group is fuzzy S-quasinormally embedded if and only if its level subset is S-quasinormally embedded in the usual sense of group theory. Secondly, the homomorphic properties of fuzzy S-quasinormally embedded subgroups are discussed. Finally, the homomorphic properties are extended to fuzzy S-quasinormal subgroups.
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