Let 0:Z50-Z15 be a group homomorphism with 0(x)=4x. Then, Ker(Ø)= {0, 10, 20, 30, 40)
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Q: Let ø:Z50→Z15 be a group homomorphism with ø(x)=4x. Then, Ker(ø)= * None of the choices
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- 9. Suppose that and are subgroups of the abelian group such that . Prove that .25. Prove or disprove that every group of order is abelian.27. a. Show that a cyclic group of order has a cyclic group of order as a homomorphic image. b. Show that a cyclic group of order has a cyclic group of order as a homomorphic image.
- Exercises 3. Find an isomorphism from the additive group to the multiplicative group of units . Sec. 16. For an integer , let , the group of units in – that is, the set of all in that have multiplicative inverses, Prove that is a group with respect to multiplication.Let H1={ [ 0 ],[ 6 ] } and H2={ [ 0 ],[ 3 ],[ 6 ],[ 9 ] } be subgroups of the abelian group 12 under addition. Find H1+H2 and determine if the sum is direct.Exercises 31. Let be a group with its center: . Prove that if is the only element of order in , then .