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6.45 (1978)

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Construct a characteristic subgroup $N$ of a finitely generated free group $F$ such that $F/N$ is infinite and simple. If no such exists, it would follow that $d(S^2) = d(S)$ for every infinite finitely generated simple group $S$, where $d(S)$ is the minimum number of generators. There is reason to believe that this is false.

Contributor: J. Wiegold

Progress

Editors’ comment: It is proved that for all $n \geqslant 2$, the free group $F_n$ admits continuum many pairwise non-isomorphic infinite simple characteristic quotients (R. Coulon, F. Fournier-Facio, https://arxiv.org/abs/2312.11684).

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