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A characterization of generalized cyclic group
Naseem Ajmal,Nusrat Sultana,Iffat Jahan 원광대학교 기초자연과학연구소 2018 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.16 No.2
This paper demonstrates that a generalized cyclic group can be characterized in terms of the distributivity of its $L$-subgroup lattice wherein the join structure of a pair of $L$-subgroups is formulated with the help of the notion of tip extended pair of $L$-subgroups. Also using this join structure, the modularity of the lattice of normal $ L $-subgroups of a group $G$ is established. In the last section, we establish our main theorems by an application of subdirect product theorems.