7. find order of all the elements of the group = {1, −1, ?, −?} . the binary operator ∗ is defined as ? ∗ ? = ??.
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7. find order of all the elements of the group = {1, −1, ?, −?} . the binary operator ∗ is defined as ? ∗ ? = ??.
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- 38. Let be the set of all matrices in that have the form with all three numbers , , and nonzero. Prove or disprove that is a group with respect to multiplication.For each of the following values of n, find all distinct generators of the group Un described in Exercise 11. a. n=7 b. n=5 c. n=11 d. n=13 e. n=17 f. n=1945. Let . Prove or disprove that is a group with respect to the operation of intersection. (Sec. )
- Let A={ a,b,c }. Prove or disprove that P(A) is a group with respect to the operation of union. (Sec. 1.1,7c)True or False Label each of the following statements as either true or false. An element in a group may have more than one inverse.6. For each of the following values of , describe all the abelian groups of order , up to isomorphism. b. c. d. e. f.