# Homework Help: Abstract algebra

1. May 19, 2010

### tyrannosaurus

1. The problem statement, all variables and given/known data
What is the minimum number of generators needed for Z2+Z2+Z2? Find a set of generators and relations for this group.

2. Relevant equations

3. The attempt at a solution
I think it is obvious that the minimum amount of generators that you need is three, with Z2+Z2+Z2 = {a,b,c|a^2=b^2=c^2} but I don't know what I have to put down for the relations in the group and I am not sure how to explain that the minimum is 3 generators. Any help would be great!!!

2. May 19, 2010

### Dick

It's not 'obvious' that the minimal number of generators is three until you explain why you think it is. And I have no idea what Z2+Z2+Z2 = {a,b,c|a^2=b^2=c^2} is supposed to mean. Can you explain?

3. May 20, 2010

### eok20

To show that you can't have two generators: what do you know about the order of elements in the group?

In terms of the relations, you definitely need more than just a^2=b^2=c^2=e since the group with that presentation is infinite. What about relations to make the group abelian?