Right. Consider , then,
and
But are normal subgroups of ,so:
and for all .
which implies for all .
As a consequence, is a normal subgroup of .
Regards.
Fernando Revilla
Show that if K and N are normal subgroups of G, then K intersect N is normal to G.
We have gkg^-1 is in K and gng^-1 is in N.
I think I know the basic idea:
Take a h in the intersection and take an arbitrary g.
I need to show g^-1hg is in the intersection
I guess I'm stuck in showing that. I guess maybe I don't understand what taking that h means.
Right. Consider , then,
and
But are normal subgroups of ,so:
and for all .
which implies for all .
As a consequence, is a normal subgroup of .
Regards.
Fernando Revilla