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The pseudocomplementedness of modular lattices described by two 0-sublattices

In this article, we first characterize pseudocomplemented inductive modular lattices by using their two 0-sublattices. Then we use two 0-sublattices of a subgroup lattice to describe all locally cyclic abelian groups. In particular, we show that a locally cyclic abelian group can be characterized by its three subgroups.