# Thread: Need help with a factor group

1. ## Need help with a factor group

Giventhe group (Z24, +). Consider the subgroup U={ [0]24,[4]24,[8]24,[12]24,[16]24,[20]24}.Determine the elements of Z24/U .

2. ## Re: Need help with a factor group

Originally Posted by uniculdan
Giventhe group (Z24, +). Consider the subgroup U={ [0]24,[4]24,[8]24,[12]24,[16]24,[20]24}.Determine the elements of Z24/U .
Surely you know that the elements of $\mathbb{Z}_{24}/U$ are just the cosets of $U$ in $\mathbb{Z}_{24}~?$

3. ## Re: Need help with a factor group

Originally Posted by Plato
Surely you know that the elements of $\mathbb{Z}_{24}/U$ are just the cosets of $U$ in $\mathbb{Z}_{24}~?$
Here is the original text.

4. ## Re: Need help with a factor group

Originally Posted by uniculdan
Here is the original text.
Even from the German, it is not clear to me form of the answer your textbook/instructor wants.
Can you give us the element $11+[12]_{24}~?$

Can you give us the coset $11+U~?$

5. ## Re: Need help with a factor group

[12]24={...-60, -36, -12, 12, 36, 60,...}. So 11+[12]24={...-49, -25, -1, 33, 47, 71...}=[23]24

6. ## Re: Need help with a factor group

Originally Posted by uniculdan
[12]24={...-60, -36, -12, 12, 36, 60,...}. So 11+[12]24={...-49, -25, -1, 33, 47, 71...}=[23]24
Well done! Now tell us why you cannot finish the exercise?