Characterization of Certain Groups and Fuzzy Subgroups

Abstract

Fuzzy subgroups of Hamiltonian, solvable, P-Hall, and nilpotent groups are examined. The notions of generalized characteristic fuzzy subgroups, fully invariant fuzzy subgroups, and characteristic fuzzy subgroups are introduced. It is shown that if G is a finite group all of whose Sylow subgroups are cyclic, then a fuzzy subgroup of a group G is normal if and only if it is a generalized fuzzy subgroup of G. Normal fuzzy subgroups, quasi-normal fuzzy subgroups, (p, q)-subgroups, fuzzy cosets, fuzzy conjugates and SL(p, q)-subgroups are also presented. The results of this chapter are mainly from the work of Asaad and Abou-Zaid [9, 11, 12, 13, 14].