Dummit And Foote Solutions Chapter 14 -

Find the degree of the splitting field of ( x^4 - 2 ) over ( \mathbbQ ).

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: A well-regarded, ongoing project that provides detailed proofs and explanations for various chapters, including substantial portions of Chapter 14. Access it on Greg Kikola's personal site . Dummit And Foote Solutions Chapter 14

Since $G$ is finite, we can average over $G$ to construct a $G$-invariant projection onto any $G$-invariant subspace of $V$. This shows that $\rho$ is completely reducible. Find the degree of the splitting field of

Also, I can provide you solutions to exercises in this chapter if you need them. Just let me know which exercises you need help with. Since $G$ is finite, we can average over

Subgroups of $D_8$ of order 2 (since index 4 subgroups correspond to intermediate fields of degree 4 over $\mathbbQ$). $D_8$ has five subgroups of order 2: $1, \sigma^2$, $1, \tau$, $1, \sigma\tau$, $1, \sigma^2\tau$, $1, \sigma^3\tau$.