Unformatted text preview: G . 4. We stated in class that if G , H and K are nite groups and G H = G K then H = K . Show that if we allow G to be innite then H need not be isomorphic to K . 5. Dirichlets theorem say that, for every pair of relatively prime integers a and b , there are innitely many primes of the form at + b . Use Dirichlets theorem to prove that every nite Abelian group is isomorphic to a subgroup of U ( n ) for some n . (Note: If m and n are relatively prime then U ( mn ) = U ( m ) U ( n ).)...
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 Spring '11
 Johnson
 Algebra, Multiplication, Prime number, Abelian group, Cyclic group, Group isomorphism, Abelian

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