Abstract Algebra: Theory and Applications · Problem 9.4.16

Normal Subgroups and Factor Groups — Thomas Judson

Mathematics — Abstract Algebra · direct-products-order

Problem

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

(3, 4)

\mathbb{Z}_4 \times \mathbb{Z}_6

((b))

(6, 15, 4)

\mathbb{Z}_{30} \times \mathbb{Z}_{45} \times \mathbb{Z}_{24}

((c))

(5, 10, 15)

\mathbb{Z}_{25} \times \mathbb{Z}_{25} \times \mathbb{Z}_{25}

((d))

(8, 8, 8)

\mathbb{Z}_{10} \times \mathbb{Z}_{24} \times \mathbb{Z}_{80}

Hint. (a) 12; (c) 5.