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# group theory question watch

1. Need help on aiii

what does it mean by conjugate? or do I just power all of y by a?

Also can someone tell me if I got these right please.

ai) a b^-1 a^2 b a b a^-1

aii) b^-3 a^-1 b^-1 a
2. (Original post by cooldudeman)

Need help on aiii

what does it mean by conjugate? or do I just power all of y by a?

Also can someone tell me if I got these right please.

ai) a b^-1 a^2 b a b a^-1

aii) b^-3 a^-1 b^-1 a
Holy moly. Is that uni stuff?
3. (Original post by Andy98)
Holy moly. Is that uni stuff?
yep
4. (Original post by cooldudeman)
yep
No wonder I don't get it
5. (Original post by cooldudeman)
ai) a b^-1 a^2 b a b a^-1

aii) b^-3 a^-1 b^-1 a
Can't help with aiii - don't even know what means.

aii however is incorrect, try forming using that.

Recall
6. (Original post by cooldudeman)

Need help on aiii
From a bit of digging I suspect you are looking for the element:

You should have a definition of the symbology in your notes somewhere.
7. (Original post by ghostwalker)
From a bit of digging I suspect you are looking for the element:

You should have a definition of the symbology in your notes somewhere.
so aii is a b^-1 a^-1 b^-3 right?

and thanks for aiii, but I will ask my lecturer just in case.

For b, what does it mean by conjugate? I cannot for the life of me find the definition in my notes!
8. (Original post by Andy98)
Holy moly. Is that uni stuff?
Tots get you man When a question barely makes sense
9. (Original post by cooldudeman)
so aii is a b^-1 a^-1 b^-3 right?

and thanks for aiii, but I will ask my lecturer just in case.

For b, what does it mean by conjugate? I cannot for the life of me find the definition in my notes!

Two elements x,y are conjugate if there exists an element, say a, such that or putting it another way , and I suspect with the notation used in your photo, that's
10. (Original post by ghostwalker)

Two elements x,y are conjugate if there exists an element, say a, such that or putting it another way , and I suspect with the notation used in your photo, that's
so is it like aza^-1=z' = a^2 b^2 ab^-1 ab^-1 ?

Also for 3c, is it like we find aza^-1=z' and a^-1 za=z' and bzb^-1=z' and b^-1 zb=z'
??
11. (Original post by cooldudeman)
so is it like aza^-1=z' = a^2 b^2 ab^-1 ab^-1 ?
Well, at the end z has a^-1 already, so you'd end up with a^-2 at the end

Also for 3c, is it like we find aza^-1=z' and a^-1 za=z' and bzb^-1=z' and b^-1 zb=z'
??
I suspect so. Those are certainly conjugate, but:

Conjugacy is an equivalence relation, and you could do etc, but then there would be an infinite number of possibilities.

But since you're expected to list them all, that can't be the case.
I don't know what's expected there - I'd need to see some of the background material, or someone else may be familiar with this and more able to help.
12. (Original post by ghostwalker)
Well, at the end z has a^-1 already, so you'd end up with a^-2 at the end

I suspect so. Those are certainly conjugate, but:

Conjugacy is an equivalence relation, and you could do etc, but then there would be an infinite number of possibilities.

But since you're expected to list them all, that can't be the case.
I don't know what's expected there - I'd need to see some of the background material, or someone else may be familiar with this and more able to help.
Thanks at least for helping. I will ask around uni.

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