Abstract Algebra: Theory and Applications · Problem 9.4.8

Normal Subgroups and Factor Groups — Thomas Judson

Mathematics — Abstract Algebra · isomorphism-proof-or-disproof

Problem

Prove that

\mathbb{Q}

is not isomorphic to

\mathbb{Z}

. Hint. Assume that

\mathbb{Q}

is cyclic and try to find a generator.