English
The derived series of a group G is the sequence of subgroups defined by D_0 = ⊤ and D_{n+1} = [D_n, D_n], where [A,B] denotes the commutator subgroup of A and B.
Русский
Производящая серия группы G — это последовательность подгрупп D_0 = ⊤ и D_{n+1} = [D_n, D_n], где [A,B] обозначает commutator-подгруппу A и B.
LaTeX
$$$\\mathrm{derivedSeries}: \\mathbb{N} \\to \\text{Subgroup}(G),\\; D_0 = \\top,\\; D_{n+1} = [D_n,D_n].$$$
Lean4
/-- The derived series of the group `G`, obtained by starting from the subgroup `⊤` and repeatedly
taking the commutator of the previous subgroup with itself for `n` times. -/
def derivedSeries : ℕ → Subgroup G
| 0 => ⊤
| n + 1 => ⁅derivedSeries n, derivedSeries n⁆
