feat(src/group_theory/specific_groups/alternating.lean): prove that the alternating group is perfect
Prove what is said: the alternating group on α,
with 5 ≤ fintype.card α, is perfect, aka equal to its commutator subgroup.
Prove two intermediate lemmas, that 3-cycles are commutators
and are contained in the commutator subgroup
Prove two ugly lemmas that should be (and certainly will) golfed by people
more competent than me.
Author
Antoine Chambert-Loir
Committer
Antoine Chambert-Loir