Unformatted text preview: two in S 6 . (2 points) 3. Let G be a group of order 21 with Z ( G ) = 1. Prove that G has exactly 5 conjugacy classes. (3 points) 4. Let G be a group with exactly two elements x , y of order 2. Prove that either x ∈ Z ( G ) or  G : C G ( x )  = 2. Deduce that C G ( x ) ± G . (3 points) 5. Section 4.4, Exercise 3 on page 137. (2 points) (5 problems, 13 points altogether)...
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 Fall '07
 PALinnell
 Math, Algebra, Group Theory, Symmetric group, Coset, Group isomorphism, Conjugacy class, Index of a subgroup

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