Abstract Algebra: Theory and Applications · Problem 30

Permutation Groups — Thomas Judson

Mathematics — Abstract Algebra · cyclic-groups-subgroups

Problem

Suppose that

G

is a group and let

a, b \in G

. Prove that if

|a| = m

and

|b| = n

with

\gcd(m,n)=1

, then

\langle a \rangle \cap \langle b \rangle = \{e\}