| 单词 | Galois group |
| 释义 | Galois group If f is a polynomial over F, then the Galois group of f is the Galois group of its splitting field. The Galois group of f acts (see action) on the set of roots of f. A polynomial f over ℚ is solvable by radicals if and only if its Galois group is solvable. The Galois group of x5−x−1 is the symmetric group S5, which is not solvable. See Galois correspondence. |
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