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 φ (60) = φ (3) · φ (4) · φ (5) = 2 · 2 · 4 = 16. (b) By Proposition 2.7.4 (iii), the number of elements of order 10 is φ (10) = φ (2) · φ (5) = 1 · 4 = 4. (5) (a) We write the two cycles as permutations: σ = ± 1 2 3 4 2 3 1 4 ² and τ = ± 1 2 3 4 2 4 3 1 ² . Therefore στ = ± 1 2 3 4 3 4 1 2 ² and τσ = ± 1 2 3 4 4 3 2 1 ² . (b) In cycle notation, we have στ = (13)(24) and τσ = (14)(23) ....
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 Spring '08
 OGUS
 Algebra, Binomial Theorem, Factors, Binomial, −1 hg

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