Automorphism groups of finite posets II

TL;DR

This paper demonstrates that any finite group can be represented as the automorphism group of a finite poset with a specific size, and it establishes bounds for posets with cyclic automorphism groups of prime power order.

Contribution

It proves that every finite group can be realized as a poset automorphism group with 4|G| points and provides bounds for cyclic automorphism groups of prime power order.

Findings

Any finite group G can be realized as automorphism group of a poset with 4|G| points.

Bounds are established for the minimum size of posets with cyclic automorphism groups of prime power order.

Abstract

We prove that every finite group $G$ can be realized as the automorphism group of a poset with $4|G|$ points. We also provide bounds for the minimum number of points of a poset with cyclic automorphism group of a given prime power order.