# Math Help - clarification

1. ## clarification

find all the left cosets for the subgroup <[5]> ={[0],[5],[10]}in Z(15) integer 15.

im just wondering, under addition, are the left cosets
1+ <[5]> ={[1],[6].[11]} etc

or is it of the form 1<[5]> ={[0],[5],[10]}, 2<[5]> ={[0],[5],[10]},
3<[5]> ={[0]}

im not sure which it should be..

2. im unsure as to when addition in such cases means times and when its the sum..and when under the operation of multiplication, it means to the power of and when it means times...

thanks

3. Originally Posted by alexandrabel90
im unsure as to when addition in such cases means times and when its the sum..and when under the operation of multiplication, it means to the power of and when it means times...

thanks
$\mathbb{Z}_{15}$ isn't even a group under modular multiplication. Thus, you add.

4. by the way, how do i determine all the elements in S4, knowing that there will be 24 elements?

i need it to find the left coset of H and finding the elements in S4 seems like the easiest way to solve it

5. Originally Posted by alexandrabel90
by the way, how do i determine all the elements in S4, knowing that there will be 24 elements?

i need it to find the left coset of H and finding the elements in S4 seems like the easiest way to solve it
You will only need to find $\frac{24}{|H|}$ cosets.

6. besides randomly trying my luck to find out the 4 cosets, is there some other method to find out which 4 out of the 24 elements in S4 i should use to multiply with H?