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Concept
Solvable Group
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Summary
A
Solvable Group
is a type of group in
Abstract Algebra
where the group can be broken down into a series of subgroups, each one a
Normal Subgroup
of the previous, such that the
Quotient Groups
are all abelian. This property is significant because it allows for the application of the
Theory of solvability
to determine whether certain
Polynomial Equations
can be
Solved by radicals
.
Concepts
Group Theory
Normal Subgroup
Abelian Group
Quotient Group
Composition Series
Derived Series
Galois Theory
Radical Solvability
Jordan-Hölder Theorem
Simple Group
Borel Subgroups
Unipotent Group
Nilpotent Group
Commutator Subgroup
Central Series
Lower Central Series
Subgroup Series
Borel Subgroup
Algebraic Group Classification
Semisimple Group
Semisimple Algebraic Group
Relevant Degrees
Algebra 100%
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