Closure Properties in the Class of Multiple Context Free Groups

TL;DR

This paper proves that the class of groups with k-multiple context-free word problems remains closed when constructing new groups via graphs of groups with finite edge groups, expanding understanding of their algebraic structure.

Contribution

It establishes closure properties of k-multiple context-free groups under graphs of groups with finite edge groups, a new result in algebraic group theory.

Findings

Closure under graphs of groups with finite edge groups

Extension of known closure properties

Advancement in understanding group word problems

Abstract

We show that the class of groups with $k$-multiple context-free word problem is closed under graphs of groups with finite edge groups.