Many studies have investigated the lattice structure of fuzzy substructures of algebraic sets such as group and ring. Some important results about modularity and distributivity have been obtained in these studies. In this paper, we first define the notion of (normal) (λ,μ)-L-subgroups on a group and investigate some of their properties. In particular, we discuss the relationships among ordinary...

In this paper, we determine all of subgroups of symmetric group S4 by applying Lagrange theorem and Sylow theorem. First, we observe the multiplication table of S4, then we determine all possibilities of every subgroup of order n, with n is the factor of order S4. We found 30 subgroups of S4. The diagram of lattice subgroups of S4 is then presented. Mathematics Subject Classification: 20B30, 20...