About the metric approximation of Higman's group

TL;DR

This paper demonstrates that Higman's group cannot be embedded into a metric ultraproduct of finite groups when using a commutator-contractive invariant length function, highlighting limitations in metric approximations of certain infinite groups.

Contribution

It provides a novel non-embedding result for Higman's group into specific metric ultraproducts, advancing understanding of metric group approximations.

Findings

Higman's group does not embed into the specified ultraproducts.

Limits on metric approximation methods for Higman's group.

Insights into the structure of groups with invariant length functions.

Abstract

We prove that Higman's group does not embed into a metric ultraproduct of finite groups with a commutator-contractive invariant length function.