Probabilistically nilpotent groups

2018/01/22 by Shalev, Aner
#FOS: Mathematics #Group Theory (math.GR) #Primary 20E26 #Secondary 20P05

paper · doi:10.48550/arxiv.1801.07197

Abstract

We show that, for a finitely generated residually finite group Γ, the word [x₁, …, x_k] is a probabilistic identity of Γ if and only if Γ is virtually nilpotent of class less than k. Related results, generalizations and problems are also discussed.

Related

• Probabilistically-like nilpotent groups
• Probabilistic nilpotence in infinite groups
• A probabilistic approach toward the finite general linear and unitary groups
• Probabilistic properties of profinite groups
• Probabilistic Bounds on the Number of Elements to Generate Finite Nilpotent Groups and Their Applications