Algorithmic problems in Engel groups and cryptographic applications

TL;DR

This paper surveys algorithmic problems in Engel groups, exploring their theoretical aspects and potential cryptographic applications, while proposing open problems for future research.

Contribution

It introduces new algorithmic challenges in Engel groups and discusses their relevance to cryptography, highlighting areas for further investigation.

Findings

Identification of classical and novel algorithmic problems in Engel groups

Discussion of potential cryptographic applications of Engel group properties

Proposal of open problems to guide future research in the area

Abstract

The theory of Engel groups plays an important role in group theory since these groups are closely related to the Burnside problems. In this survey we consider several classical and novel algorithmic problems for Engel groups and propose several open problems. We study these problems with a view towards applications to cryptography.