Realising countable groups as automorphisms of origamis on the Loch Ness monster

TL;DR

This paper demonstrates that any countable group can be realized as the automorphism group of a compact origami surface, specifically on the Loch Ness monster, extending known results from finite groups.

Contribution

It introduces a concise argument showing that all countable groups can be represented as automorphism groups of origamis on the Loch Ness monster, broadening the scope of origami automorphism realizations.

Findings

Any countable group can be realized as an automorphism group of a Loch Ness monster origami.

The method extends finite group results to countable groups.

Origamis on the Loch Ness monster can model arbitrary countable automorphism groups.

Abstract

It is known that every finite group can be represented as the full group of automorphisms of a suitable compact origami. In this paper, we provide a short argument to note that the same holds for any countable group by considering origamis on the Loch Ness monster.