Membership problems in nilpotent groups

Abstract: The talk will focus on the Submonoid and the Rational Subset Membership problems in nilpotent groups. Whereas the Subgroup Membership is decidable in all nilpotent groups by a classical result of Malcev, both of our problems are undecidable in large enough nilpotent groups by results of Romanikov, putting nilpotent groups on the boundary between decidability and undecidability. I’ll explain a non-obvious link between the two problems. Most importantly, this link can be used to prove the existence of a nilpotent group with decidable Submonoid Membership and undecidable Rational Subset Membership. I’ll also give some ideas on how to solve both problems in a few more groups, including the Rational Subset Membership for the 3-dimensional Heisenberg group.

Mathematics

Audience: researchers in the topic

( video )

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West Switzerland Geometry, Algebra and Topology Seminar

Series comments: Introduced by Bruno Luiz Santos Correia, this seminar series focuses on talks from young (masters/phd/early-career) researchers who study/work in Switzerland.

All talks in this seminar series are related to topics in Geometry, Algebra and/or Topology.

If you are a researcher in Switzerland who would like to provide a talk at this seminar, please contact one of the organiser. (Alex Bishop or Bruno Correia)

What are people saying about the seminar:

"cringe" - Davide Perego

"what a fantastic seminar, Alex does a great job!" - Alex Bishop

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