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Unformatted text preview: r i r j , r i s j , s i r j , and s i s j . For example, r i r j = r i + j , where the addition of indices is mod n . (b) Show that D n is indeed a group. 4. Find all subgroups of D 5 . (Hint: rst prove that, if H D 5 contains a nontrivial rotation, then it contains all rotations.) 5. If G is a group, the center of G is dened to be Z ( G ) = { x G  xy = yx for all y G } . (a) Show that Z ( G ) is a subgroup of G . (b) For n 3, what is the center of D n ? (Use the multiplication rules you found above. The answer depends on whether n is even or odd.) 6. How challenging did you nd this assignment? How long did it take?...
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This note was uploaded on 03/14/2012 for the course MATH 113 taught by Professor Ogus during the Spring '08 term at University of California, Berkeley.
 Spring '08
 OGUS
 Math

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