Abstract Algebra: Theory and Applications · Problem 9.4.18

Normal Subgroups and Factor Groups — Thomas Judson

Mathematics — Abstract Algebra · internal-direct-products

Problem

Prove that the subgroup of

\mathbb{Q}^*

consisting of elements of the form

2^m 3^n

for

m, n \in \mathbb{Z}

is an internal direct product isomorphic to

\mathbb{Z} \times \mathbb{Z}