The pseudocomplementedness of modular lattices described by two 0-sublattices

TL;DR

This paper characterizes pseudocomplemented inductive modular lattices through their two 0-sublattices and applies this to describe locally cyclic abelian groups using three subgroups.

Contribution

It introduces a new characterization of pseudocomplemented inductive modular lattices via two 0-sublattices and applies this to classify locally cyclic abelian groups.

Findings

Pseudocomplemented inductive modular lattices can be characterized by two 0-sublattices.

Locally cyclic abelian groups are describable using three subgroups.

The approach links lattice properties to group structure.

Abstract

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.