Ramification structures for quotients of multi-EGS groups

TL;DR

This paper extends the class of groups known to admit ramification structures by proving that quotients of multi-EGS groups, generalizations of GGS-groups, also possess these structures, linking group theory with surface-related properties.

Contribution

It demonstrates that quotients of multi-EGS groups, a broader class than GGS-groups, admit ramification structures, expanding the understanding of their algebraic and geometric properties.

Findings

Quotients of multi-EGS groups admit ramification structures.

Extension of known results from GGS-groups to multi-EGS groups.

Provides a group-theoretic characterization related to surface isogeny.

Abstract

Groups associated to surfaces isogenous to a higher product of curves can be characterised by a purely group-theoretic condition, which is the existence of a so-called ramification structure. G\"{u}l and Uria-Albizuri showed that quotients of the periodic Grigorchuk-Gupta-Sidki groups, GGS-groups for short, admit ramification structures. We extend their result by showing that quotients of generalisations of the GGS-groups, namely multi-EGS groups, also admit ramification structures.