- #1

karnten07

- 213

- 0

## Homework Statement

Let m[tex]\in[/tex]N. We defined a binary operation on Zm:= {[tex]_{}0[/tex],[tex]_{}1[/tex]..., [tex]_{}m-1[/tex]}. Show that Zm together with this binary operation is a group. (Hint. For associativity you need to distinguish several cases)

## Homework Equations

## The Attempt at a Solution

I don't know what the lines above the numbers mean, does it mean they can be positive an negative? (there are meant to be lines above the numbers in Zm)

Example of Z3:

+ 0 1 2

0 0 1 2

1 1 2 0

2 2 0 1

For the cases i need to use to show associativity, i think they are m=1, m>1 and m>2 because my lecturer said that, although I am not sure i remember exactly what he said so i could be wrong. I can show m=1 as it is just a group table of all zeros. I think the case where m>1 it is meant to be 2>/=m>1 so it becomes Z2. But how do i show z>2 as it has elements that go up to m-1?