Besides studying some algebraic properties of intuitionistic fuzzy subgroups of a group, we prove that an intuitionistic fuzzy subgroup A of a group G is an intuitionistic fuzzy abelian (cyclic) subgroup if and only if the support of A is an abelian (cyclic) subgroup of G.

intuitionistic fuzzy set (IFS), intuitionistic fuzzy subgroup (IFSG), intuitionistic fuzzy normal subgroup (IFNSG), intuitionistic fuzzy abelian subgroup (IFASG), intuitionistic fuzzy cyclic subgroup (IFCSG), support of intuitionistic fuzzy set.