Abstract Algebra: Theory and Applications · Problem 14.5.20

The Sylow Theorems — Thomas Judson

Mathematics — Abstract Algebra · faithful-group-action

Problem

A group acts faithfully on a

G

-set

X

if the identity is the only element of

G

that leaves every element of

X

fixed. Show that

G

acts faithfully on

X

if and only if no two distinct elements of

G

have the same action on each element of

X