Theorems · Definition · group theory

QuotientGroup.quotientMulEquivOfEq

{G : Type u} →
  [inst : Group G] → {M N : Subgroup G} → [inst_1 : M.Normal] → [inst_2 : N.Normal] → M = N → G ⧸ M ≃* G ⧸ N

If two normal subgroups M and N of G are the same, their quotient groups are isomorphic.

Defined in

Mathlib.GroupTheory.QuotientGroup.Basic

Cited by

5 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupSubgroup.NormalSubgroup.Normal