Abstract Algebra: Theory and Applications · Problem 6.5.1

Introduction to Cryptography — Thomas Judson

Mathematics — Abstract Algebra · lagrange-theorem

Problem

Suppose that

G

is a finite group with an element

g

of order 5 and an element

h

of order 7. Why must

|G| \geq 35

? Hint. The order of

g

and the order

h

must both divide the order of

G