NORMAL FUZZY SUBGROUPS AND FUZZY NORMAL SERIES OF FINITE-GROUPS

It is known that, for every normal fuzzy subgroup of a finite group, there exists a series of normal subgroups of this group. Here we prove that the length of this chain is two only. Also, we define the maximal normal fuzzy subgroup and give some of its properties in analogy to the crisp case. Also, we give the necessary and sufficient condition for it to be the derived group contained in the 1-level subgroup of a normal fuzzy subgroup. We define the subnormal, normal, and composition series of normal fuzzy subgroups and explain the interrelationship between them and the series in the crisp case.