Question

True or false: A group of order n contains an element of order n. Justify your answer.

Short answer

The statement is false. Consider the group ${\mathrm{\mathbb{Z}}}_2\times {\mathrm{\mathbb{Z}}}_2$.

Step-by-step solution

Determine the statement True or False

Consider the Statement, A group of order n contains an element of order n.

The above statement is false.

Justification

Let’s consider the group${\mathrm{\mathbb{Z}}}_2\times {\mathrm{\mathbb{Z}}}_2$ of order 4 . The element of this group have order is 2.