Unformatted text preview: formulas for R i R j , R i F j , F i R j , and F i F j . For example, R i R j = R i + j , where the addition of indices is mod n . 5. Find all subgroups of D 4 . 6. If G is a group, the center of G is deﬁned 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 > 2, what is the center of D n ? (Use the multiplication rules you found above. The answer depends on whether n is even or odd.) 7. Fraleigh section 6, exercise 32 (justify as always). 8. How challenging did you ﬁnd this assignment? How long did it take?...
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This note was uploaded on 02/16/2010 for the course MATH 113 taught by Professor Ogus during the Spring '08 term at Berkeley.
 Spring '08
 OGUS
 Math

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