 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ia/paper-3/6d/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

With

D_{8} = ⟨ r, s : r^{4} = s^{2} = 1, srs = r^{- 1} ⟩

, its normal subgroups are

1, ⟨ r^{2} ⟩, ⟨ r ⟩, ⟨ r^{2}, s ⟩, ⟨ r^{2}, rs ⟩, D_{8} .

The last three proper nontrivial examples have index two; the four individual reflection subgroups are not normal.

 New to topics? Read the docs here!