Let f: Q8 to D8 be a homomorphism from the quaternion Q8 to thedihedral group D8 of order 8. Suppose that f (i) = rs and f( j) =r^2.
(a) Find f (k) and f(-k) (expressed in standard form r^i*s^i forsuitable i and j) ·
(b) List the elements in the kernel of f in standard form.
(c) The quotient group Q8/ker(f) is isomorphic to which one ofthe groups C2, C4 or C2xC2 Â Â Â why?
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