Abstract Algebra: Theory and Applications · Problem 9.4.27

Normal Subgroups and Factor Groups — Thomas Judson

Mathematics — Abstract Algebra · isomorphism-cyclic

Problem

Let

G \cong H

. Show that if

G

is cyclic, then so is

H

. Hint. Let

a

be a generator for

G

. If

\phi : G \to H

is an isomorphism, show that

\phi(a)

is a generator for

H