Two Algorithms in Group Theory

TL;DR

This paper introduces a new algorithm to determine the finiteness of intersections of quasiconvex subgroups with conjugates in negatively curved groups and provides a proof for the decidability of membership problems in such contexts.

Contribution

It presents a novel algorithm for subgroup intersection finiteness and offers a concise proof for membership problem decidability in quasiconvex subgroups.

Findings

Algorithm successfully determines finiteness of subgroup intersections.

Decidability of membership problem established for quasiconvex subgroups.

Provides a simplified proof of membership problem decidability.

Abstract

We present a new algorithm deciding if the intersection of a quasiconvex subgroup of a negatively curved group with a conjugate is finite. We also give a short proof of decidability of the membership problem for quasiconvex subgroups of finitely generated groups with decidable word problem.