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Equations in Burnside groups

· 2021 · math.GR · arXiv 2112.07409

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abstract

This article is a first step in the study of equations in periodic groups. As an application, we study the structure of periodic quotients of hyperbolic groups. We investigate for instance the Hopf and co-Hopf properties, the isomorphism problem, the existence of free splittings, etc. We also consider the automorphism group of such periodic groups.

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representative citing papers

Power quotients of surface groups and mapping class groups

math.GR · 2025-07-18 · conditional · novelty 8.0

For sufficiently large n, the automorphism and outer automorphism groups of the n-power quotient of a hyperbolic surface group are isomorphic to the corresponding power quotients of the extended mapping class group, and these quotients are infinitely presented, acylindrically hyperbolic, and…

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  • Power quotients of surface groups and mapping class groups math.GR · 2025-07-18 · conditional · none · ref 23 · internal anchor

    For sufficiently large n, the automorphism and outer automorphism groups of the n-power quotient of a hyperbolic surface group are isomorphic to the corresponding power quotients of the extended mapping class group, and these quotients are infinitely presented, acylindrically hyperbolic, and…