 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2015/prelims/mathematics-i/6/a/i/solution

Let

∣ G ∣ = p

, with

p

g \neq = e

g

divides

p

and is greater than one. It is therefore

p

, and

G = ⟨ g ⟩

. Hence a group of prime cardinality is a cyclic group.

The converse is false: the cyclic group

C_{4}

has four elements, and

4

 New to topics? Read the docs here!