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In "A proof of the Scott–Wiegold conjecture on free products of cyclic groups" Howie proved that every one-relator product of three cyclic groups is nontrivial. Is there a now proven theorem that says every two-relator product of ($\geq$)n cyclic groups is nontrivial for some n? If not, how much is known about this?

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  • $\begingroup$ Perhaps it's worth remarking that Howie conjectures that this should be true for n=5. $\endgroup$
    – HJRW
    Commented Jun 23, 2014 at 10:47

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