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## Main Question or Discussion Point

Hey everyone

Let's say I have two generators, [itex]a[/itex] and [itex]b[/itex], with the following relations:

[itex]a^{5}=b^{2}=E[/itex]

[itex]bab^{-1}=a^{-1}[/itex];

Where E is the Identity element.

What I've done so far is this - the number of elements of the group is the product of the exponents of both generators, which is 10. Then I listed all the elements and their products which aren't equal to Identity. So I got the group elements:

{[itex]{E , a , a^{2} , a^{3} , a^{4} , ab , a^{2}b , a^{3}b , a^{4}b , b}[/itex]}

So is that right? The only thing that's confusing me is the second relation; not sure why its there really if u can get the group elements without it.

Thanks guys!

Let's say I have two generators, [itex]a[/itex] and [itex]b[/itex], with the following relations:

[itex]a^{5}=b^{2}=E[/itex]

[itex]bab^{-1}=a^{-1}[/itex];

Where E is the Identity element.

What I've done so far is this - the number of elements of the group is the product of the exponents of both generators, which is 10. Then I listed all the elements and their products which aren't equal to Identity. So I got the group elements:

{[itex]{E , a , a^{2} , a^{3} , a^{4} , ab , a^{2}b , a^{3}b , a^{4}b , b}[/itex]}

So is that right? The only thing that's confusing me is the second relation; not sure why its there really if u can get the group elements without it.

Thanks guys!