Abstract Algebra: Theory and Applications · Problem 11.4.5

Matrix Groups and Symmetry — Thomas Judson

Mathematics — Abstract Algebra · homomorphisms-between-cyclic-groups

Problem

Describe all of the homomorphisms from

\mathbb{Z}_{24}

\mathbb{Z}_{18}

. Hint. For any homomorphism

\phi : \mathbb{Z}_{24} \to \mathbb{Z}_{18}

, the kernel of

\phi

must be a subgroup of

\mathbb{Z}_{24}

and the image of

\phi

must be a subgroup of

\mathbb{Z}_{18}

. Now use the fact that a generator must map to a generator.