Define the commutator magma of a group to be the magma whose elements are the same as the group’s and whose operation is the group’s commutator.
What are the conditions for two finite groups to have isomorphic commutator magmas?
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2$\begingroup$ This is quite broad; it would be useful if you include your observations so far. $\endgroup$– YCorCommented Dec 5, 2022 at 10:41
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$\begingroup$ Clearly commutator magmas are isomorphic if the original groups are isomorphic. Abelian groups of equal cardinality also have isomorphic commutator magmas. Two natural next things to consider would be (finite) nilpotent groups of class 2; and perfect groups. No idea what happens then. $\endgroup$– Max HornCommented Aug 14, 2023 at 22:40
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