Gaps in probabilities of satisfying some commutator-like identities

2018/09/09 by Delizia, Costantino, Jezernik, Urban, Moravec, Primoz +1
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1809.02997

Abstract

We show that there is a positive constant δ< 1 such that the probability of satisfying either the 2-Engel identity [X₁, X₂, X₂] = 1 or the metabelian identity [[X₁, X₂], [X₃, X₄]] = 1 in a finite group is either 1 or at most δ.

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