Solvable groups

theorem that a generic equation of degree 5 or higher cannot be solved by radicals

group that can be constructed from abelian groups using extensions; a group whose derived series terminates in the trivial subgroup

in mathematics, a solvable group that satisfies the maximal condition on subgroups

group that has an invariant normal series where all the factors are cyclic groups

subgroup whose order is coprime to its index

mathematical object

group G with abelian normal subgroup N and abelian quotient group G/N (equivalently: group with abelian commutator subgroup)