The compressed word problem in relatively hyperbolic groups

TL;DR

This paper demonstrates that the compressed word problem can be efficiently solved in groups that are hyperbolic relative to free abelian subgroups, expanding understanding of computational problems in geometric group theory.

Contribution

It proves polynomial-time solvability of the compressed word problem for relatively hyperbolic groups with free abelian subgroups, a new result in the field.

Findings

Compressed word problem is solvable in polynomial time for these groups.

Extends computational group theory to a broader class of relatively hyperbolic groups.

Provides new algorithms for group-theoretic decision problems.

Abstract

We prove that the compressed word problem in a group that is hyperbolic relative to a collection of free abelian subgroups is solvable in polynomial time.