Recent content by Lengalicious

Of course, sorry, this is just the 1st ever problem I've attempted in group theory and its a struggle to get my head around. From the definition of the left coset is it correct to say ##cS_G(a)=\{d~\epsilon~ G:\exists~ g ~\epsilon~ S_G(a):d=cg\}## so ##dad^{-1}=cgad^{-1}## ?

Is this what I am finding? The conjugates of elements in the centralizer? http://www.proofwiki.org/wiki/Conjugates_of_Elements_in_Centralizer

Is there a different definition for a coset of a centralizer vs a coset of a standard subgroup? And I think you are correct about the 2nd typo, I have emailed my professor to check though.

I'm really confused still, does the left coset commute with any of the elements? also does it obey any group axioms, or is this not relevant Am I supposed to start with d or d^-1 = something and keep doing valid operations on it until i get to dad^-1 = something?

Thanks for the hints and clarification

I have updated the opening post with an attachment of the question, hopefully its more clear

Homework Statement I need to determine dad^1 for each element d in the left-coset formed by acting on the elements in C_G(a) with the element c such that c is not an element of the subgroup C_G(a) Homework Equations The Attempt at a Solution I don't really understand what the...

Ok so if I did that then what? I can define a characteristic equation such that r^2-\frac{a}{1+bx}=0 and r=\pm\sqrt{\frac{a}{1+bx}} where b^2-4ac = 4a(1+bx) > 0 so a solution is y=ce^{rx} but that doesn't satisfy the ODE so its not correct?

Homework Statement Solve (1+bx)y''(x)-ay(x)=0Homework Equations The Attempt at a Solution I'm used to solving homogeneous linear ODE's where you form a characteristic equation and solve that way, here there is the function of x (1+bx) so how does that change things?

not really sure I understand, am I correct in using D=ae^{rx} and subbing that into(1+bx)\frac{D''}{D}=\sigma to find r? Or is my r incorrect? EDIT: I see what you mean nevermind.. EDIT: I don't suppose you could give me a hint on how to find the trial solution? I have not come across an ODE...

Homework Statement See attachment (stuck with part b at the moment)Homework Equations The Attempt at a Solution \phi=D(x)T(t) so (1+bx)D''(x)T(t)-D(x)T''(t)=0 (1+bx)\frac{D''(x)}{D(x)}=\frac{T''(t)}{T(t)} let \frac{T''}{T}=\sigma (1) use trial solution T=be^{rt} subbing into (1) and solve...

Thanks guys!

Yeah, that was my initial thought, just confuses me why the question uses z.. ooh well thanks I can actually get somewhere if I sub a in.

Sorry for being unclear, I found the radius of convergence to be \rho_o=|a| using the ratio test, forgot to include that in the opening post. I am unclear as to how I am supposed to figure the behaviour based on this information, the question literally gets me to find the radius of convergence...

Homework Statement Series: \sum_{n=1}^{\infty}(-1)^{(n+1)}\frac{(x)^n}{na^n} what is the behaviour of the series at radius of convergence \rho_o=-z ? Homework Equations The Attempt at a Solution So I can specify that the series is monatonic if z is non negative as...