Computational aspects of subindices and subfactors with characterization of finite index stable groups

TL;DR

This paper explores the computational properties of subindices and subfactors in groups, combining theoretical and computational methods to characterize finite index stable groups and address open problems in the field.

Contribution

It introduces new computational approaches and fully characterizes finite index stable groups, advancing understanding in group theory and related areas.

Findings

Complete characterization of finite index stable groups

Development of computational methods for subindices and subfactors

Resolution of several open problems in the theory

Abstract

Recently, sub-indices and sub-factors of groups with connections to number theory, additive combinatorics, and factorization of groups have been introduced and studied. Since all group subsets are considered in the theory and there are many basic open problems, conjectures, and questions, their computational aspects are particularly important. In this paper, by introducing some computational methods and using theoretical approaches together, we not only solve several problems but also pave the way to study the topic. As the most important result of the study, we completely characterize finite index stable groups.