Dummit And Foote Solutions Chapter 14 !link!

Compute the Galois group of $\mathbbQ(\sqrt2, \sqrt3)$ over $\mathbbQ$.

Working through the exercises in Chapter 14 is a rite of passage for many graduate students. The solutions are not just about finding "x"; they are about constructing rigorous proofs . Common exercises involve: Computing Galois Groups: Taking a polynomial like and finding its Galois group over the rational numbers Mapping Subgroups to Intermediate Fields: Dummit And Foote Solutions Chapter 14

, you primarily only need to worry about normality (splitting fields). Use the tower rule to determine the size of the Galois group. Compute the Galois group of $\mathbbQ(\sqrt2, \sqrt3)$ over