Reference no: EM131046932
1. Let Rx = R - {0} and set G = Rx x R. Define * on G by the following:
(a, b)*(c, d) = (ac, bc + d)
Show that G is a group under *. Is it abelian?
2. Let G be a group and let φ: S3 → G be a non-trivial homomorphism. Suppose φ is not injective. Find the kernel of φ. If φ is surjective, what is G?
3. Assume that G is a group with a subgroup H such that |H| = 6, [G : H] > 4 , and |G| < 50 . What are the possibilities for |G|?
4. Define new addition ⊕ and multiplication ? on Z by
a ⊕ b= a + b - 1, and a ? b = a + b - ab
where operations on the right hand side of the equal signs are ordinary addition, subtraction and multiplication. Show that Z with these new operations, ⊕ and ?, is an integral domain.
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What are telomeres and what is the function
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Type of no-fault auto insurance laws to compensate
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What factors can affect the goals you set
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What is meant by map
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Find the kernel
: Let G be a group and let φ: S3 → G be a non-trivial homomorphism. Suppose φ is not injective. Find the kernel of φ. If φ is surjective, what is G
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Which most likely would yield the most predictable evidence
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Identify factors that may interfere with training goals
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Why was it not followed up
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Organizations such as events like graduations
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