- #1
AdrianZ
- 319
- 0
Homework Statement
If H is any subgroup of G and [itex]N={\cap_{a\in G} a^{-1}Ha}[/itex], prove that N is a normal subgroup of G.
The Attempt at a Solution
Is this statement true? [itex]\forall n: n \in N \implies \exists h \in H : n=a^{-1}ha[/itex]
The theorem looks intuitively true, but I don't know how to write a formal argument knowing that [itex]N={\cap_{a\in G} a^{-1}Ha}[/itex]