proof of the third isomorphism theorem@Everything2.com

This proof sketch of the third isomorphism theorem uses the symbols in my writeup there without repetition of the formulation, so you may want to read that first.

Define the natural epimorphism f: G -> G/N by f(g) = gN. Consider its restriction h = f|H to H. Clearly, Ker h = L (the intersection of H and N). But since G=HN, h is an epimorphism (indeed, for any coset gN with g in G, g=hn for h in H, n in N, so gN=hN).

The theorem follows by applying the first isomorphism theorem to h.

third isomorphism theorem	first isomorphism theorem	epimorphism	Proof of Wedderburn's theorem about finite division rings
How to kiss like a ninja	Saint Peter	VCD	Po
symbol	mathematics

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