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The dihedral group D6 is generated by an element a of order 6, and an element b of order 2, satisfying the relation (*) baa6-1b (i) Determine number of group homomorphisms f : Z→ D6. (ii) Determine the number of group homomorphisms g: Z9 → Dg

The dihedral group D6 is generated by an element a of order 6, and an element b of order 2, satisfying the relation (*) baa6-1b (i) Determine number of group homomorphisms f : Z→ D6. (ii) Determine the number of group homomorphisms g: Z9 → Dg

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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The dihedral group D6 is generated by an element a of order 6, and an element b of order 2, satisfying the relation (*) ba = a-¹b (i) Determine number of group homomorphisms f : Z → D6. (ii) Determine the number of group homomorphisms g: Z9 → Dg Hint: What can you can about the order of f(x) where X is an element of G? Also, for (ii) you might want to make use of the relation (*).
Transcribed Image Text:The dihedral group D6 is generated by an element a of order 6, and an element b of order 2, satisfying the relation (*) ba = a-¹b (i) Determine number of group homomorphisms f : Z → D6. (ii) Determine the number of group homomorphisms g: Z9 → Dg Hint: What can you can about the order of f(x) where X is an element of G? Also, for (ii) you might want to make use of the relation (*).
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