## walters 2 years ago consider the groups Z3 and U(9) list the element of Z3 multiply U(9)

1. beketso

Z3 ={0,1,2} U(9) = {1,2,4,5,7,8}

2. beketso

now are u supposed to multiply Z3 by U(9)?

3. experimentX

looks like both of you are on same school

4. walters

List the element of$z _{3}$multiply U(9)

5. walters

yes i must multiply z3 by u(9)

6. experimentX

what is Z3 and U9 ??

7. beketso

is it multiply or cross(X)

8. walters

z3 set of integers and u(9) means u find the number from 1 to 9 that cannot divide 9 or and those number must never divide each other

9. experimentX

under what operation is it a group?

10. walters

multiplication

11. experimentX

how?? Z3 is not closed under multiplication

12. walters

check question 3

13. walters

i don't know whether tht x mean multiplication or cross

14. experimentX

question no??

15. walters

question 3 3.1 a

16. beketso

you should take an element from Z3 and combine it with an element from U9

17. walters

"by combine wat do u mean "

18. experimentX

LOL Q 5.4 came in my exam

19. walters

z3={0,1,2} u(9)={1,2,4,5,7,8}

20. beketso

Take an the first element from z3 and combine it with all elements in u9

21. walters

then z3 x u(9)={0,1,2,4,5,7,8}

22. beketso

u get (0,1) (0,2) (0,4) (0,5) (0,7) (0,8)

23. beketso

then u have to do the same with the second element of Z3

24. walters

ok

25. walters

oh becuase u came with a new set how will u get the identity because the new set is different to z3 and u(9)

26. experimentX
27. experimentX

looks like by group U(n), you mean $$\Bbb Z \mod n$$ what is the convention followed for Z in your book?

28. walters

but the way beketso did this it is not easy to get z3 cross u(9)

29. beketso

by U(n) we mean a set of numbers which are relatively prime to n and are smaller than n

30. experimentX

you sure on that?? (how is it closed on operation if it has no mechanism to reduce elements greater than it) and what is Z?? check your book again ... what convention is followed

31. beketso

z3 x U9 ={(0,1) (0,2) (0,4) (0,5) (0,7) (0,8) (1,1) (1,2) (1,4) (1,5) (1,7) (1,8) (2,1) (2,2) (2,4) (2,5) (2,6) (2,8) } The first element is from z3 and the second is from U(9)

32. beketso

@experimentX Z is the set of integers and Zn is Z mod n

33. experimentX

what's the operation? it talks about cyclic group

34. walters

i think since we r in z multiplication and addition are closed .

35. experimentX

since you have taken Cartesian product, $$\Bbb Z_3 \times U(9)$$ how do you define this new group? What book are you following for abstract algebra?

36. walters

First course in abstract algebra by fraleigh

37. walters

i think it will be closed under *

38. beketso

am not sure but i think it is the combination of the identity element from Z3 and the identity element from U9 So, the identity element is (0,1)

39. walters

because by addition ther is a high possibility wen u add 2 integar u find the resul will no longer suits u(9)

40. beketso

on which operation is U9 a group?

41. walters

42. walters

because by multiplication it won't hold ie 5*7 is not in u(9)

43. beketso

5*7 = 8 which is in U(9)

44. walters

so it means the operation is either + or *

45. walters

7+8 is also 8 wen working with addition

46. beketso

7+8 = 6 in U(9) which is not in the set

47. beketso

that is why i think the identity element is (0,1)

48. walters

it can't be the values will circulate in {1,2,4,5,7,8} only there is no way we can get any value except those who are in u(9)

49. walters

we can use the fact that says most of the time wen the first elementin a set is 0 in the the the operation that likely to be closed is + and if the fist element is 1 * is likely to be closed

50. experimentX

your text book is very nice. the problem looks like it's related to Group Action on sets

51. walters

because u r saying the identity is (0,1) so meaning the operation will be *

52. experimentX

but it's morning here ... i gotta get some sleep. will see later

53. walters

it is also morning to me see u

54. experimentX

it's 7 am in the morning!!

55. walters

to me is 3:12 am

56. beketso

@walters will do this more later

57. experimentX

see ya later .. will see this tomorrow.