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What is the transitive group details of a polynomial where only the third power terms occur? That is $x^{3n} + a_{n-1} x^{3(n-1)} + ... + a_1 x^3 + a_0$. I need the basic theorems that state or prove this group structure. I think that the answer is $C_{3} \wr {S}_{n}$ from other examples however I do not understand this answer well. Likewise I need the theorem for the quadratic case of just even powers occurring.

Thanks in advance!

daOnlyBG
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menkelh
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  • Do you mean the Galois group of such polynomials? – lhf Feb 27 '15 at 01:07
  • Yes the Galois groups are my focus. – menkelh Feb 27 '15 at 01:27
  • I encountered an example that simply stated that even power equations of the form ${x}^{2n}+{a}{n-1}{x}^{2(n-1)}+\cdots+{a}{1}{x}^{2}+{a}{0}$ are generic to the hyperoctahedral group ${C}{2} \wr {S}{n} = {S}{2,n} = {B}_{n}$. OK, this is good, however I need some theorems that make this statement firm and there may be additional restraints and conditions that I am unaware of. – menkelh Feb 27 '15 at 23:00

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