Nilpotent fuzzy subgroups
Summary: In this paper, we introduce a new definition for nilpotent fuzzy subgroups, which is called the good nilpotent fuzzy subgroup or briefly g-nilpotent fuzzy subgroup. In fact, we prove that this definition is a good generalization of abstract nilpotent groups. For this, we show that a group \(G\) is nilpotent if and only if any fuzzy subgroup of \(G\) is a g-nilpotent fuzzy subgroup of \(G\). In particular, we construct a nilpotent group via a g-nilpotent fuzzy subgroup. Finally, we characterize the elements of any maximal normal abelian subgroup by using a g-nilpotent fuzzy subgroup.
scientific article; zbMATH DE number 6916901
scientific article