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10.13 (1986)

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Does there exist a massive set of independent elements in a free group $F_2$ on free generators $a, b$, that is, a set $E$ of irreducible words on the alphabet $a, b, a^{-1}, b^{-1}$ such that
$\qquad$ 1) no element $w \in E$ belongs to the normal closure of $E \setminus \{w\}$, and
$\qquad$ 2) the massiveness condition is satisfied: $\overline{\lim}\limits_{n \to \infty} \sqrt[n]{\lvert E_n \rvert} = 3$, where $E_n$ is the set of all words of length $n$ in $E$?

Contributor: R. I. Grigorchuk

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