Is the set of numbers described below a group under the given operation? Even integers; addition O Yes O No
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A set is called group on binary operation if
a) It is closed
b) It is associative
c) It has identity element
d) each element has an inverse
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- Let a,b,c, and d be elements of a group G. Find an expression for (abcd)1 in terms of a1,b1,c1, and d1.Construct a multiplication table for the group G of rigid motions of a rectangle with vertices 1,2,3,4 if the rectangle is not a square.If a is an element of order m in a group G and ak=e, prove that m divides k.
- 12. Find all homomorphic images of each group in Exercise of Section. 18. Let be the group of units as described in Exercise. For each value of, write out the elements of and construct a multiplication table for . a. b. c. d.True or False Label each of the following statements as either true or false. In a Cayley table for a group, each element appears exactly once in each row.