The words x^d and [x,y]^d are rigid: any word inducing the same measures on all finite groups is an automorphic image of them.
Automorphism-invariant positive definite functions on free groups
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abstract
In this article we raise some new questions about positive definite functions on free groups, and explain how these are related to more well-known questions. The article is intended as a survey of known results that also offers some new perspectives and interesting observations; therefore the style is expository.
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math.GR 1years
2019 1verdicts
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Some Orbits of Free Words that are Determined by Measures on Finite Groups
The words x^d and [x,y]^d are rigid: any word inducing the same measures on all finite groups is an automorphic image of them.