(1 point) The dihedral group D5 is generated by an element a of order 5, and an

Question

(1 point) The dihedral group D5 is generated by an element a of order 5, and an element b of order 2, satisfying the relation

()     ba=a51b

(1 point) The dihedral group Ds is generated by an element al of order 5, and an element b of order 2, satisfying the relation (*) ba=a51b (i) Determine number of group homomorphisms f : Z D5. (ii) Determine the number of group homomorphisms g : 2,9 D9 Hint: What can you can about the order of f(x) where z is an element of G? Also, for (i) you might want to make use of the relation *)

Explanation / Answer

a=5&b=2

ba=a5-1b

2x5=5-1(2)

10=5-2

10=3

a=5& b=2

ba=a5-1b

2x5=5^42

10=625x2

10=1250

answer 125

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