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

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beketsoBest ResponseYou've already chosen the best response.0
Z3 ={0,1,2} U(9) = {1,2,4,5,7,8}
 one year ago

beketsoBest ResponseYou've already chosen the best response.0
now are u supposed to multiply Z3 by U(9)?
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
looks like both of you are on same school
 one year ago

waltersBest ResponseYou've already chosen the best response.0
List the element of\[z _{3}\]multiply U(9)
 one year ago

waltersBest ResponseYou've already chosen the best response.0
yes i must multiply z3 by u(9)
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
what is Z3 and U9 ??
 one year ago

beketsoBest ResponseYou've already chosen the best response.0
is it multiply or cross(X)
 one year ago

waltersBest ResponseYou've already chosen the best response.0
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
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
under what operation is it a group?
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
how?? Z3 is not closed under multiplication
 one year ago

waltersBest ResponseYou've already chosen the best response.0
i don't know whether tht x mean multiplication or cross
 one year ago

beketsoBest ResponseYou've already chosen the best response.0
you should take an element from Z3 and combine it with an element from U9
 one year ago

waltersBest ResponseYou've already chosen the best response.0
"by combine wat do u mean "
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
LOL Q 5.4 came in my exam
 one year ago

waltersBest ResponseYou've already chosen the best response.0
z3={0,1,2} u(9)={1,2,4,5,7,8}
 one year ago

beketsoBest ResponseYou've already chosen the best response.0
Take an the first element from z3 and combine it with all elements in u9
 one year ago

waltersBest ResponseYou've already chosen the best response.0
then z3 x u(9)={0,1,2,4,5,7,8}
 one year ago

beketsoBest ResponseYou've already chosen the best response.0
u get (0,1) (0,2) (0,4) (0,5) (0,7) (0,8)
 one year ago

beketsoBest ResponseYou've already chosen the best response.0
then u have to do the same with the second element of Z3
 one year ago

waltersBest ResponseYou've already chosen the best response.0
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)
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
http://www.physicsforums.com/showthread.php?t=474271
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
looks like by group U(n), you mean \( \Bbb Z \mod n \) what is the convention followed for Z in your book?
 one year ago

waltersBest ResponseYou've already chosen the best response.0
but the way beketso did this it is not easy to get z3 cross u(9)
 one year ago

beketsoBest ResponseYou've already chosen the best response.0
by U(n) we mean a set of numbers which are relatively prime to n and are smaller than n
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
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
 one year ago

beketsoBest ResponseYou've already chosen the best response.0
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)
 one year ago

beketsoBest ResponseYou've already chosen the best response.0
@experimentX Z is the set of integers and Zn is Z mod n
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
what's the operation? it talks about cyclic group
 one year ago

waltersBest ResponseYou've already chosen the best response.0
i think since we r in z multiplication and addition are closed .
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
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?
 one year ago

waltersBest ResponseYou've already chosen the best response.0
First course in abstract algebra by fraleigh
 one year ago

waltersBest ResponseYou've already chosen the best response.0
i think it will be closed under *
 one year ago

beketsoBest ResponseYou've already chosen the best response.0
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)
 one year ago

waltersBest ResponseYou've already chosen the best response.0
because by addition ther is a high possibility wen u add 2 integar u find the resul will no longer suits u(9)
 one year ago

beketsoBest ResponseYou've already chosen the best response.0
on which operation is U9 a group?
 one year ago

waltersBest ResponseYou've already chosen the best response.0
because by multiplication it won't hold ie 5*7 is not in u(9)
 one year ago

beketsoBest ResponseYou've already chosen the best response.0
5*7 = 8 which is in U(9)
 one year ago

waltersBest ResponseYou've already chosen the best response.0
so it means the operation is either + or *
 one year ago

waltersBest ResponseYou've already chosen the best response.0
7+8 is also 8 wen working with addition
 one year ago

beketsoBest ResponseYou've already chosen the best response.0
7+8 = 6 in U(9) which is not in the set
 one year ago

beketsoBest ResponseYou've already chosen the best response.0
that is why i think the identity element is (0,1)
 one year ago

waltersBest ResponseYou've already chosen the best response.0
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)
 one year ago

waltersBest ResponseYou've already chosen the best response.0
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
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
your text book is very nice. the problem looks like it's related to Group Action on sets
 one year ago

waltersBest ResponseYou've already chosen the best response.0
because u r saying the identity is (0,1) so meaning the operation will be *
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
but it's morning here ... i gotta get some sleep. will see later
 one year ago

waltersBest ResponseYou've already chosen the best response.0
it is also morning to me see u
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
it's 7 am in the morning!!
 one year ago

beketsoBest ResponseYou've already chosen the best response.0
@walters will do this more later
 one year ago

experimentXBest ResponseYou've already chosen the best response.0
see ya later .. will see this tomorrow.
 one year ago
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