Group theory Q (1 Viewer)

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The question reads :

"What is the order of a group G generated by elements a and b subject only to the relations

[tex] a^7 = 1 [/tex] , [tex] b^3 = 1 [/tex] , [tex] ba = a^rb [/tex]"

I know that the order is the number of elements in the group.

I'm having a lot of trouble answering a lot of these questions.
Any help would be greatly appreciated.

Thanks in advance.
 

Hurkyl

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Well, you could always write down all of the elements of the group.
 
Hurkyl said:
Well, you could always write down all of the elements of the group.
How do you go about doing that using the information given? I don't know where to begin.

Also, does [itex] a^7 = 1 [/itex] mean a to the 7 is equal to the identity element?
 

Hurkyl

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Well, there's a, and aa, and aaa, and ab, and ba, and aba, and bab, and abbaabbab, and...


Yes, the relation a^7 = 1 means that aaaaaaa is the identity.
 
I think I see where this is going.

Does [itex]a^8 = a^7 * a = 1 * a[/itex] make sense?
 
ElDavidas said:
I think I see where this is going.

Does [itex]a^8 = a^7 * a = 1 * a[/itex] make sense?
Yup. And use the ba relation to reorder your products so that they all read "aaaa....bb..."

-Dan
 

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