Is every finitely generated simple group $2$-generated?
This happens to be true for finite simple groups and for Tarski monster groups, but is it true in general? I do not know how to prove that, but neither do I know any counterexamples.
2026-03-25 04:54:44.1774414484
Is every finitely generated simple group $2$-generated?
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I haven't read it thoroughly enough to understand the construction, but this 1986 paper by Guba constructs a finitely generated simple group all of whose $2$-generated subgroups are free, and which is therefore not itself $2$-generated. From the introduction it seems that the question you asked was open until then.