Weakly surjunctive groups and symbolic group varieties
Algebraic Geometry
2021-12-07 v2 Combinatorics
Dynamical Systems
Group Theory
Rings and Algebras
Abstract
In this paper, we introduce the classes of weakly surjunctive and linearly surjunctive groups which include all sofic groups and more generally all surjunctive groups. We investigate various properties of such groups and establish in particular a reversibility and invertibility theorem for injective endomorphisms of symbolic group varieties over weakly surjunctive group universes with algebraic group alphabets in arbitrary characteristic. We also obtain novel evidence related to Kaplansky's stable finiteness conjecture.
Cite
@article{arxiv.2111.13607,
title = {Weakly surjunctive groups and symbolic group varieties},
author = {Xuan Kien Phung},
journal= {arXiv preprint arXiv:2111.13607},
year = {2021}
}
Comments
Include the new Section 7 on weakly dual surjunctive groups