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(left- and right-; not sure which counts as which) conjugate(s) y ∙ x ∙ (y ⁻¹), (y ⁻¹) ∙ x ∙ y; (obviously interdefinable, but at the cost of having to repeatedly invoke ⁻¹-involutive)
(both flavours of) commutator y ∙ x ∙ (y ⁻¹) ∙ (x ⁻¹), (x ⁻¹) ∙ (y ⁻¹) ∙ x ∙ y; (ditto.)
Mal'cev operation(s) x ∙ (y ⁻¹) ∙ z;
where, in each case, we have to choose a suitable bracketing... Plus... properties?
Outstanding issue from #2252 , #2247 / #2251 : where should these new operations live?