 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2015/ia/paper-3/7d/b/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-06

False. Use the same subgroups of

S_{3}

HeH = H

has two elements, while

H (13) H

has four. Thus even a fixed pair of subgroups can give different double-coset sizes. Their disjoint union is all six elements of

S_{3}

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