Abelianization

Stream: maths

[Yury G. Kudryashov]

Hi, I'm going to redefine docs#abelianization using docs#con so that it works for monoids.

[Yury G. Kudryashov]

While looking at the existing code, I noticed that we have docs#subgroup.commutator (notation instance for Lie bracket on subgroups), docs#commutator_element (notation instance for Lie bracket on elements), and docs#commutator (the commutator subgroup). Does any of these notions have a commonly used synonym in English?

[Thomas Browning]

I'm partly to blame for this. Here's my understanding of the terminology:
1) docs#commutator_element is "the commutator of the elements g₁ and g₂"
2) docs#subgroup.commutator is "the commutator of the subgroups H₁ and H₂" (generated by (1))
3) docs#commutator is "the commutator subgroup of G" (a special case of (2))
My personal feeling is that the names of (1) and (2) don't matter so much, since they are just instances for the commutator bracket notation, so we might as well give the short name commutator to (3). But another option would be to rename (3) to commutator_subgroup.