1. Let * be defined on R by letting a + b = \abl. Determine whether the binary operation * gives a group structure. If n

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1 Let Be Defined On R By Letting A B Abl Determine Whether The Binary Operation Gives A Group Structure If N 1 (50.74 KiB) Viewed 61 times

1. Let * be defined on R by letting a + b = \abl. Determine whether the binary operation * gives a group structure. If no group results, give all axioms from the definition of groups that do not hold. 2. Let S = {a e Ra+ -1}. Define * on S by a+b= a + b + ab. a. Show that * gives a binary operation on S. b. Show that (S, *) is a group. c. Find the solution of the equation 2*1*3 = 7 in S. 3. Let n be a positive integer and let nZ = {nm me Z}. a. Show that n2, +) is a group. b. Show that (nZ, +) - (Z, +), i.e., these two groups are isomorphic. 4. Compute the indicated product involving the following permutations in Se. 2 3 4 5 6 1 2 3 4 5 6 14 5 6 2 4 1 3 6 5 0- T 2) 3 a. to b. 0-27 5. Write the group table for D3.