 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ia/paper-3/6d/c/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

An element of order three in

S_{7}

3 1^{4}

3^{2} 1

. There are

(3 7) (3 - 1)! = 35 \cdot 2 = 70

single three-cycles. For two disjoint three-cycles, choose the two unordered three-element supports and an orientation on each:

\frac{1}{2} (3 7) (3 4) (2) (2) = 280.

Hence

S_{7}

contains

350

elements of order three.

 New to topics? Read the docs here!