A characterization of generalized cyclic group
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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.
Abstract
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.
참고문헌 (24)
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