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Unformatted text preview: , x 3 (mod 10) and x 7 (mod 15) . (3) Prove that every subgroup of an abelian group is normal. (4) Consider the product of cyclic groups G = Z / 3 Z Z / 4 Z Z / 5 Z . (a) Show that the group G is cyclic. (b) How many elements in G are generators of G ? (c) How many elements in G have order 10? (5) The cycles = (123) and = (124) are in the symmetric group S 4 . (a) Compute the two products and in S 4 . (b) Write both and as products of disjoint cycles....
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 Spring '08
 OGUS
 Math, Algebra

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