Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Algebra proof question help

Very confused on this proof, not sure how to construct the proof of these 3 questions :/

Original post by maths10101

Very confused on this proof, not sure how to construct the proof of these 3 questions :/

Let's say that if we have

g \in G

, then

g^n = e

where n is the order of g. This also means that

g^k \neq e

where

1 \leq k < n

.

Now we have:

e' = f(e) = f(g^n) = f(g)^n

, now can you use the fact that

f

is a bijection, along with

g^k \neq e

to get your result?

where have all the purists gone?
where is
DFranklin
ghostwalker
Davros
Smaug123

to name a few

Original post by TeeEm

where have all the purists gone?
where is
DFranklin
ghostwalker
Davros
Smaug123

to name a few

Smaug is still around, I think, but busy with Part III. Not sure where the others have disappeared to.

Original post by Zacken

Smaug is still around, I think, but busy with Part III. Not sure where the others have disappeared to.

I remembered another one fireGarden or something... gone too

OP

Original post by Zacken

Let's say that if we have

g \in G

, then

g^n = e

where n is the order of g. This also means that

g^k \neq e

where

1 \leq k < n

.

Now we have:

e' = f(e) = f(g^n) = f(g)^n

, now can you use the fact that

f

is a bijection, along with

g^k \neq e

to get your result?

Oh okay, I'm slowly starting to understand it..is this for part a right? And would that be the full proof or would you think there's more?

Original post by maths10101

Oh okay, I'm slowly starting to understand it..is this for part a right? And would that be the full proof or would you think there's more?

Yes, for part (a). For part(b) find an element that does not obey the thing proved in part(a) to show that they aren't isomorphic.

If you fill in the blanks I left, that's the full proof, it's not very long. Just needs some heavy ideas.

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