In the area of abstract algebra

Abstract algebra

Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...

 known as group theory

Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...

, a 2-transitive group is a transitive permutation group

Permutation group

In mathematics, a permutation group is a group G whose elements are permutations of a given set M, and whose group operation is the composition of permutations in G ; the relationship is often written as...

 in which a point stabilizer acts transitively on the remaining points. Every 2-transitive group is a primitive group, but not conversely. Every Zassenhaus group

Zassenhaus group

In mathematics, a Zassenhaus group, named after Hans Julius Zassenhaus, is a certain sort of doubly transitive permutation group very closely related to rank-1 groups of Lie type.- Definition :...

 is 2-transitive, but not conversely. The solvable

Solvable group

In mathematics, more specifically in the field of group theory, a solvable group is a group that can be constructed from abelian groups using extensions...

 2-transitive groups were classified by Bertram Huppert

Bertram Huppert

Bertram Huppert is a German mathematician specializing in group theory and the representation theory of finite groups. His Endliche Gruppen is an influential textbook in group theory, and he has over 50 doctoral descendants.-Education:Bertram Huppert went to school in Bonn from 1934 until 1945...

 and are described in the list of transitive finite linear groups. The insoluble groups were classified by using the classification of finite simple groups

Classification of finite simple groups

In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group belongs to one of four categories described below. These groups can be seen as the basic building blocks of all finite groups, in much the same way as the prime numbers are the basic...

 and are all almost simple group

Almost simple group

In mathematics, a group is said to be almost simple if it contains a non-abelian simple group and is contained within the automorphism group of that simple group: if it fits between a simple group and its automorphism group.More precisely, a group is almost simple if it is isomorphic to such a group...

s.