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math.GR2026
Asymptotic Burnside laws
Gil Goffer, Be'eri Greenfeld, Alexander Yu. Olshanskii
We construct novel examples of finitely generated groups that exhibit seemingly-contradicting probabilistic behaviors with respect to Burnside laws. We construct a finitely generat…
math.GR2025
Linear average-case complexity of algorithmic problems in groups
Alexander Olshanskii, Vladimir Shpilrain
The worst-case complexity of group-theoretic algorithms has been studied for a long time. Generic-case complexity, or complexity on random inputs, was introduced and studied relati…