Normal Subgroups of G: K ∩ N is Normal

[kathrynag]

Homework Statement

Show that if K and N are normal subgroups of G, then K intersect N is normal to G.

Homework Equations

The Attempt at a Solution

K and N are normal.
Then:
gkg^-1 is in K
gng^-1 is in N
want to show the intersection is a normal subgroup of G.
My problem is how to deal with the intersection

 

[micromass]

Take a h\in K\cap N (what does this mean?) and take an arbitrary g.
You'll need to show that g^{-1}hg\in K\cap N (so, what do you need to show?)

 

[kathrynag]

Take a h in the intersection of two normal subgroups is what that means