solvable extension

solvable extension

[′säl·və·bəl ik′sten·chən]
(mathematics)
A finite extension E of a field F such that the Galois group of the smallest Galois extension of F containing E is a solvable group.
References in periodicals archive ?
In [6], Kahrobaei proved the generalized free product of two finitely generated solvable groups amalgamated by central subgroups is a solvable extension of a residually solvable group and, hence, is residually solvable.
By Theorem 6, K is free and, consequently, G is a solvable extension of a free group.
Therefore, G is a solvable extension of a free group and is, thus, residually solvable.