Communications of the
Korean Mathematical Society CKMS

The various fuzzy subgroups of a group which are admissible under operator domains are studied. In particular, the classes of all inner automorphisms, automorphisms, and endomorphisms are applied on the fuzzy subgroups of a group. As results, several theorems and examples concerning the fuzzy subgroups following from these kinds of operator domains are obtained. Moreover, we prove that a necessary condition for a fuzzy subgroup to be characteristic is that the center of the fuzzy subgroup is characteristic.

Keywords: fuzzy subgroup, level subset, support, operator domain, fuzzy normal subgroup, fuzzy characteristic subgroup, fuzzy fully invariant subgroup

MSC numbers: 20N25