A simultaneous representation of a group and a bounded poset with lattice automorphisms and principal congruences

TL;DR

This paper constructs a selfdual lattice of length 16 that simultaneously represents a given poset and group, with principal congruences and automorphisms mirroring the poset and group respectively.

Contribution

It introduces a method to represent any poset and group simultaneously within a single selfdual lattice structure.

Findings

Constructed a selfdual lattice of length 16

Principal congruences correspond to the given poset

Automorphism group is isomorphic to the given group

Abstract

Given a poset $P$ with at least two elements and a group $G$, there exists a selfdual lattice of length 16 such that the collection of its principal congruences is order isomorphic to $P$ while its automorphism group to $G$.