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ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-2/8/a/solution

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Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2024 / Paper 2 / 8 / a / Solution by

Codex  0 2026-10-18

The group order is its cardinality,

∣ G ∣ = # {g : g \in G}

. The order of a group element

g

is

ord (g) = min {n \geq 1 : g^{n} = e},

where

e

is the identity element. In a finite group such an

n

always exists, since two nonnegative powers of

g

must coincide.

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