Galois realizability of groups of order 64
β Scribed by Helen G. Grundman; Tara L. Smith
- Book ID
- 111488620
- Publisher
- SP Versita
- Year
- 2010
- Tongue
- English
- Weight
- 272 KB
- Volume
- 8
- Category
- Article
- ISSN
- 1895-1074
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We describe methods for the construction of polynomials with certain types of Galois groups. As an application we deduce that all transitive groups G up to degree 15 occur as Galois groups of regular extensions of Q(t), and in each case compute a polynomial f β Q[x] with Gal(f ) = G.
Using the representation theory of groups, we are able to give simple necessary and sufficient conditions regarding the structure of the Galois groups of second and third order linear differential equations. These allow us to give simple necessary and sufficient conditions for a second order linear