关键词: 根式塔, 根式扩张, 分裂域, 可解群

Abstract: Let f(x)∈F［x-be a polynomial over a field F, and suppose that E is a splitting field of f(x) over F. Using Galois theory and solvable group, we give some sufficient and necessary conditions for E to be a radical tower of F. It is proved that E is a radical tower of F if and only if, (1) Galois group Gal(E／F) is solvable; (2) E contains a primitive p-th root of unity for every prime divisor p of ［E:F］.

Key words: solvable group, splitting field, radical tower, radical extension