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Post Number: 3
Posted on Wednesday, 09 March, 2011 - 06:52 am:   

Let G be a group and H subgroup of G. Let T
be the set of right cosets of H in G. Then G acts
on T
by right multiplication : we define R : G -> Sym(T) : g-> Rg where Rg(x) = Xg for all X in T and and all g in G.
Prove that ker(R)= the intersection of x^-1Hx ...
I have no idea how to start this problem....I am wondering if any body will give me hint

thank you
Prolific poster

Post Number: 261
Posted on Wednesday, 09 March, 2011 - 02:45 pm:   

Write down what the definition of a kernel means in this case
New poster

Post Number: 4
Posted on Thursday, 17 March, 2011 - 03:53 am:   

Let G be a fi nite group, N normalsubgroup G and n in N such that G/N has an element of order n.
Prove that G has an element of order n.
can some body help me with this problem
so far
I let gN be an element in G/N. Then (gN)^n = g^nN which emplies that
g^n in N. I do not know what to do from here ....
can some body help....
Regular poster

Post Number: 33
Posted on Friday, 18 March, 2011 - 09:04 pm:   

This is a different question to the original post I think? If you have an element [inline]gN[/inline] of order [inline]n[/inline] in [inline]G/N[/inline] then, as you say, [inline](gN)^n =N[/inline] and [inline](gN)^k \neq N[/inline] for all [inline]k<n[/inline], and you're right that this means [inline]g^n\in N[/inline] (and moreover [inline]g^k \notin N[/inline] for all [inline]k<n[/inline]). What does this tell you about the order of [inline]g[/inline]? How small could it possibly be?

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