Fuzzy Caley's Theorem and Fuzzy Lagrange's Theorem

Abstract

We begin our discussion with properties of normal fuzzy subgroups. Fuzzy analogs of some group theoretic concepts such as cosets, characteristic subgroups, conjugate fuzzy subgroups, quotient groups are then presented. We show a number of results using these fuzzified notions. The order of a fuzzy subgroup is discussed as is the notion of a solvable fuzzy subgroup. The fuzzification of Caley's Theorem and Lagrange's Theorem are also presented. In this chapter, we consider primarily, although not exclusively, the work presentedin [4, 10, 11].