Solvable Group
A solvable group is a group whose composition indices are all Prime Numbers. Equivalently, a solvable group isa Group having a ``normal series'' such that each ``normal factor'' is Abelian. The termsolvable derives from this type of group's relationship to Galois's Theorem, namely that the Symmetric Group
is insoluble for 
while it is solvable for 
, 2, 3, and 4. As a result, the Polynomial equations ofdegree 
are not solvable using finite additions, multiplications, divisions, and root extractions.
Every Finite Group of order 
, every Abelian Group, and every Subgroup of a solvable group is solvable.
References
Lomont, J. S. Applications of Finite Groups. New York: Dover, p. 26, 1993.
- Least Common Multiple
- Least Deficient Number
- Least Period
- Least Prime Factor
- Least Squares Fitting
- Least Squares Fitting--Exponential
- Least Squares Fitting--Logarithmic
- Least Squares Fitting--Power Law
- Least Upper Bound
- Lebesgue Constants (Fourier Series)
- Lebesgue Constants (Lagrange Interpolation)
- Lebesgue Covering Dimension
- Lebesgue Dimension
- Lebesgue Integrable
- Lebesgue Integral
- Lebesgue Measurability Problem
- Lebesgue Measure
- Lebesgue Minimal Problem
- Lebesgue-Radon Integral
- Lebesgue Singular Integrals
- Lebesgue-Stieltjes Integral
- Lebesgue Sum
- Le Cam's Identity
- Leech Lattice
- Lefshetz Fixed Point Formula