Question

Answer to (a) is image = Z2 • {0,2} (where • is the external direct product). And the kernel is {e,r^2} (where r is the rotation). Answer to (c) is isomorphic to Z2 • Z2. Please show work. I’m given answers but need to see how to get there. Thanks

(20 poiants) Amer aocat (a) (5 points) Identify the kernel and image of the homomorphism from D, to Z2 Z1 (the infinite cyclic group) given by the rules p(r) (1,0 and (f)-(0,2). b) (10 points) Show that no homomorphism from Ds to Z is surjective. (c) (5 points) Using the definition of φ from part (a), what well-known group is G/ker φ isomorphic to?

Answer 1

Nou

Hence ⓑ gfトossible let th, γ e exist

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