If D n is the dihedral group with generators a of order n and b of order
Question:
If Dn is the dihedral group with generators a of order n and b of order 2, then
(a) a2 ϵ Dn'.
(b) If n is odd, Dn' ≅ Zn.
(c) If n is even, Dn' ≅ Zm, where 2m = n.
(d) Dn is nilpotent if and only if n is a power of 2.
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ANSWER Solution a Recall that the commutator of two elements g and h in a group G is defined as g h ghgh Then Dn is the subgroup of Dn generated by the commutators a a and a b for 1 i j n and i j Now ...View the full answer
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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