We show that nilpotent profinite groups satisfy a word equation with positive Haar measure, confirming a conjecture.
We show that in a nilpotent profinite group, the set of answers of a word equation has nonempty interior, provided that this set has a positive Haar measure. This fact shows that the conjecture proposed by Lévai and Pyber is true for nilpotent profinite groups.
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Meisam Soleimani Malekan (2026) studied this question.
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