4 articles
Composition series
A composition series of a group is a finite chain of subgroups, each normal in the next, whose simple quotients are its composition factors, unique by the Jordan–Hölder theorem.
Feit–Thompson theorem
The Feit–Thompson theorem, also called the odd order theorem, states that every finite group of odd order is solvable, proved by Walter Feit and John Thompson in 1963.
Nilpotent group
A nilpotent group is a group whose lower central series, built by repeatedly taking commutators, reaches the trivial subgroup after finitely many steps; class 1 groups are exactly abelian.
Solvable group
A solvable group, also called a soluble group, is a group built up from abelian groups by a finite chain of extensions, central to Galois theory.