Abstract Algebra: Find Generators & Relations for Z2+Z2+Z2

[tyrannosaurus]

Homework Statement

What is the minimum number of generators needed for Z2+Z2+Z2? Find a set of generators and relations for this group.

Homework Equations

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!

 

[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?

 

[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?