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Vijay posted an Question
October 08, 2020 • 15:53 pm 30 points
  • IIT JAM
  • Mathematics (MA)

Consider the multiplicative group zs* of non-zero integers modulo 5 and additive group z4. let d: ( z4, +)-(zs*, x) be a map defined as d(m) = 3" o d is not a h

Consider the multiplicative group Zs* of non-zero integers modulo 5 and additive group Z4. Let d: ( Z4, +)-(Zs*, x) be a map defined as d(m) = 3" O d is not a homomorphism co is a homomorphism but not one- O one mapp o is a homomorphism but not onto O map is a homomorphism and bijective O map

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    Deepak singh 1 best-answer

    see attached proof , option d is correct if any doubt then ask

    cropped5609105233373850599.jpg
  • Srinath best-answer

    Option D. They both have four elements, so we can check for bijection. The range of this function is equal to the codomain. So, it is onto. And, clearly it is one-one, because kernel consists, only 0 from Z4. But before all these, try proving whether it is an homomorphism or not.

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