Do you know an example of a $2$-locally nipotent group $G$ which is not locally nilpotent?
$2$-locally nilpotent: every subgroup which is generated by $2$ elements is nilpotent.
locally nilpotent: every finitely generated subgroup is nilpotent.
2026-03-25 04:34:56.1774413296
Nilpotent groups and 2-generated subgroups
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The groups referred to in YCor's answer to this question are infinite $d$-generator $p$-groups in which every $(d-1)$-generator subgroup is finite, and hence nilpotent since it is a $p$-group. So they provide examples, although it might be hard to find out much about them.