Let : G H be a group homomorphism. Prove that Kery = {e} if and only if is injective.
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Q: 39 Find the sum of the series sin x + 3 sin 3x +5 sin 5x +...+(2k − 1) sin (2k-1)x
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Q: 4. Solve dy d.x. 3y² - x² XU . Note: your solution may be left in implicit form.
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Q: 2k+1 2. ΣK=12k²(K+1)² 3. Σ=1 tan-1(k + 1) – tan^1(k)
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- Exercises 31. Let be a group with its center: . Prove that if is the only element of order in , then .If H and K are arbitrary subgroups of G, prove that HK=KH if and only if HK is a subgroup of G.Label each of the following statements as either true or false. Two groups can be isomorphic even though their group operations are different.