Details

Autor(en) / Beteiligte

• Escofier, Jean-Pierre

Titel

Solvable Groups

Ist Teil von

• Galois Theory, p.195-206

Ort / Verlag

New York, NY: Springer New York

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• This chapter and the next one are devoted to the problem of resolving algebraic equations by radicals. Given a polynomial with coefficients in a field K, together with its splitting field N over K, the solvability of the equation P(x) = 0 by radicals can be expressed in terms of the existence of a particular sequence of intermediate extensions between K and N (see Chapter 12). By the Galois correspondence, this translates to a property of Galois group Gal(N|K). In this chapter, we introduce the groups having this special property, called solvability.