On commutativity of intuitionistic L-fuzzy groups

In this paper, we discuss the commutativity of an intuitionistic L-fuzzy subgroup of a group. Some necessary and sufficient conditions for an intuitionistic L-fuzzy subgroup to be commutative are derived. The relationship between commutativity and normality of intuitionistic L-fuzzy subgroups is briefly studied. It is also proved that any commutative intuitionistic L-fuzzy subgroup of a finite group admits a decomposition as a direct product of intuitionistic L-fuzzy subgroups of Sylow subgroups.