- #1
Dixanadu
- 254
- 2
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!