Abstract Algebra: Theory and Applications · Problem 34

Permutation Groups — Thomas Judson

Mathematics — Abstract Algebra · cyclic-groups-abelian

Problem

Let

G

be an abelian group of order

pq

where

\gcd(p,q)=1

. If

G

contains elements

a

and

b

of order

p

and

q

respectively, then show that

G

is cyclic.