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Dicn = (r,s | 2,¹s-2, rsrs-1). (a) Prove that Dic, has at most 4n elements. (In fact, it has exactly 4n elements.) (b) Use von Dyck's theorem to prove that there is a surjective homomorphism : Dicn → Dn.

Dicn = (r,s | 2,¹s-2, rsrs-1). (a) Prove that Dic, has at most 4n elements. (In fact, it has exactly 4n elements.) (b) Use von Dyck's theorem to prove that there is a surjective homomorphism : Dicn → Dn.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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The dicyclic group Dicn is defined by the presentation Dicn (r,s|r²¹, ¹-2, rsrs¯¹). (a) Prove that Dic, has at most 4n elements. (In fact, it has exactly 4n elements.) (b) Use von Dyck's theorem to prove that there is a surjective homomorphism : Dicn → Dn. =
Transcribed Image Text:The dicyclic group Dicn is defined by the presentation Dicn (r,s|r²¹, ¹-2, rsrs¯¹). (a) Prove that Dic, has at most 4n elements. (In fact, it has exactly 4n elements.) (b) Use von Dyck's theorem to prove that there is a surjective homomorphism : Dicn → Dn. =
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