## walters Group Title consider the groups Z3 and U(9) list the element of Z3 multiply U(9) one year ago one year ago

1. beketso Group Title

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

2. beketso Group Title

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

3. experimentX Group Title

looks like both of you are on same school

4. walters Group Title

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

5. walters Group Title

yes i must multiply z3 by u(9)

6. experimentX Group Title

what is Z3 and U9 ??

7. beketso Group Title

is it multiply or cross(X)

8. walters Group Title

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 Group Title

under what operation is it a group?

10. walters Group Title

multiplication

11. experimentX Group Title

how?? Z3 is not closed under multiplication

12. walters Group Title

check question 3

13. walters Group Title

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

14. experimentX Group Title

question no??

15. walters Group Title

question 3 3.1 a

16. beketso Group Title

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

17. walters Group Title

"by combine wat do u mean "

18. experimentX Group Title

LOL Q 5.4 came in my exam

19. walters Group Title

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

20. beketso Group Title

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

21. walters Group Title

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

22. beketso Group Title

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

23. beketso Group Title

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

24. walters Group Title

ok

25. walters Group Title

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 Group Title
27. experimentX Group Title

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

28. walters Group Title

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

29. beketso Group Title

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

30. experimentX Group Title

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 Group Title

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 Group Title

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

33. experimentX Group Title

what's the operation? it talks about cyclic group

34. walters Group Title

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

35. experimentX Group Title

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 Group Title

First course in abstract algebra by fraleigh

37. walters Group Title

i think it will be closed under *

38. beketso Group Title

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 Group Title

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 Group Title

on which operation is U9 a group?

41. walters Group Title

42. walters Group Title

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

43. beketso Group Title

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

44. walters Group Title

so it means the operation is either + or *

45. walters Group Title

7+8 is also 8 wen working with addition

46. beketso Group Title

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

47. beketso Group Title

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

48. walters Group Title

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 Group Title

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 Group Title

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

51. walters Group Title

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

52. experimentX Group Title

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

53. walters Group Title

it is also morning to me see u

54. experimentX Group Title

it's 7 am in the morning!!

55. walters Group Title

to me is 3:12 am

56. beketso Group Title

@walters will do this more later

57. experimentX Group Title

see ya later .. will see this tomorrow.