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Unformatted text preview: The Chinese Remainder Theorem (Section 2.8.3) implies that G is isomorphic to the group Z / 60 Z . (b) By Proposition 2.7.4 (iii), the number of generators is (60) = (3) (4) (5) = 2 2 4 = 16. (b) By Proposition 2.7.4 (iii), the number of elements of order 10 is (10) = (2) (5) = 1 4 = 4. (5) (a) We write the two cycles as permutations: = 1 2 3 4 2 3 1 4 and = 1 2 3 4 2 4 3 1 . Therefore = 1 2 3 4 3 4 1 2 and = 1 2 3 4 4 3 2 1 . (b) In cycle notation, we have = (13)(24) and = (14)(23) ....
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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 University of California, Berkeley.
 Spring '08
 OGUS
 Algebra, Binomial Theorem, Factors, Binomial

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