Abstract Algebra: Theory and Applications · Problem 4.5.2

Cyclic Groups — Thomas Judson

Mathematics — Abstract Algebra · cyclic-groups-order-of-element

Problem

Find the order of each of the following elements. ((a))

5 \in \mathbb{Z}_{12}

((b))

\sqrt{3} \in \mathbb{R}

((c))

\sqrt{3} \in \mathbb{R}^*

((d))

-i \in \mathbb{C}^*

((e))

72 \in \mathbb{Z}_{240}

((f))

312 \in \mathbb{Z}_{471}

Hint. (a) 12; (c) infinite; (e) 10.