A group acts
faithfully
on a
G
-set
X
if the identity is the only element of
G
that leaves every element of
X
xed. 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
.

Question

A group acts
faithfully
on a
G
-set
X
if the identity is the only element of
G
that leaves every element of
X
xed. 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
.

goformit100 · Answer

@uri

anonymous · Answer

@FutureMathProfessor I have a problem with the representation of the problem. I can't fully understand it because of that.

anonymous · Answer

A group G 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.