Abstract

Abstract In this paper the concepts of fuzzy subgroups and anti-fuzzy subgroups and some results involving them are generalised to the L -fuzzy case where L is an arbitrary lattice with 0 and 1. Commutativity for L -fuzzy subgroups is introduced and some necessary and sufficient conditions for an L -fuzzy subgroup to be commutative are derived. Relation between commutativity and normality of L -fuzzy subgroups is briefly studied. It is also proved that any commutative L -fuzzy subgroup of a finite group admits a decomposition as a direct product of L -fuzzy subgroups of Sylow subgroups.

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