Document Type: Proceedings of the conference "Engel conditions in groups" - Bath - UK - 2019
Department of Computer Science Deramore Lane, University of York
Department of Mathematics (University of Salerno), Italy - Department of Mathematics and Statistic (University of the Basque Country), Spain
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.