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Unformatted text preview: G  < . Prove that H must be normal. (6) Suppose that N and M are normal subgroups of G and that N T M = { e } . Prove that for any n N and m M , nm = mn , and hence that MN = M N as groups. (7) Give an example of three groups, K H G such that K is normal in H and H is normal in G , but K is not normal in G . (8) Prove that if  G  = p 2 for p a prime, then G is abelian. HINT: Try to show that Z ( G ) = G and use Cauchys and Lagranges theorems repeatedly. 1...
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 Spring '09
 DANBERWICK
 Algebra, Division

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