Unformatted text preview: , x â‰¡ 3 (mod 10) and x â‰¡ 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 Ã— Z / 4 Z Ã— 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 Ïƒ = (123) and Ï„ = (124) are in the symmetric group S 4 . (a) Compute the two products ÏƒÏ„ and Ï„Ïƒ in S 4 . (b) Write both ÏƒÏ„ and Ï„Ïƒ as products of disjoint cycles....
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This note was uploaded on 02/03/2011 for the course MATH 113 taught by Professor Ogus during the Spring '08 term at Berkeley.
 Spring '08
 OGUS
 Math, Algebra

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