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mulu1982
New poster

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
mulu1982
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....
kevinm
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 $gN$ of order $n$ in $G/N$ then, as you say, $(gN)^n =N$ and $(gN)^k \neq N$ for all $k<n$, and you're right that this means $g^n\in N$ (and moreover $g^k \notin N$ for all $k<n$). What does this tell you about the order of $g$? How small could it possibly be?