Unformatted text preview: d be a divisor of n . (a) Show that H = { R ,R d ,R 2 d ,... } is a normal subgroup of D n . (b) Describe the cosets of H in D n . (c) Show that D n /H ’ D d . (d) Show that the commutator subgroup of D 2 n is { R ,R 2 ,R 4 ,... } . (e) Show that the abelianization D ab 2 n of D 2 n is isomorphic to Z 2 × Z 2 . 5. How challenging did you ﬁnd this assignment? How long did it take?...
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 Spring '08
 OGUS
 Math, Group Theory, Normal subgroup, Cyclic group, Fraleigh section, Dn /H Dd

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