Probabilistically nilpotent groups
Copyright policy )Probabilistically nilpotent groups
We show that, for a finitely generated residually finite group $Γ$, the word $[x_1, \ldots, x_k]$ 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.
To appear in Proc. Amer. Math. Soc
- Hebrew University of Jerusalem Israel
- The Hebrew University Israel
Generators, relations, and presentations of groups, Primary 20E26, Secondary 20P05, Nilpotent groups, Probabilistic methods in group theory, FOS: Mathematics, Group Theory (math.GR), Mathematics - Group Theory, Residual properties and generalizations; residually finite groups
Generators, relations, and presentations of groups, Primary 20E26, Secondary 20P05, Nilpotent groups, Probabilistic methods in group theory, FOS: Mathematics, Group Theory (math.GR), Mathematics - Group Theory, Residual properties and generalizations; residually finite groups
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