3 papers
math.GR2025
A robust family of residually finite groups; spectra of residual finiteness growth, computability properties, and other applications (with an appendix by Arman Darbinyan and Emmanuel Rauzy)
Arman Darbinyan, Emmanuel Rauzy
In this paper, we introduce a family of residually finite groups that helps us to systematically study the residual finiteness growth function (RFG) from various perspectives. Firs…
math.GR2025
Hard Instances of Discrete Logarithm Problem and Cryptographic Applications
Christopher Battarbee, Arman Darbinyan, Delaram Kahrobaei
Let f be an arbitrary positive integer valued function. The goal of this note is to show that one can construct a finitely generated group in which the discrete log problem is poly…
math.GR2025
On what finitely generated (left-orderable) simple groups can know about their subgroups
Arman Darbinyan, Markus Steenbock
In this paper, we survey some of the recent advances on embeddings into finitely generated (left-orderable) simple group such that the overgroup preserves algorithmic, geometric, o…