Schreier conjecture
Encyclopedia
In finite group theory
, the Schreier conjecture asserts that the group of outer automorphisms of every finite simple group is solvable
. It was proposed by Otto Schreier
in 1926, and is now known to be true as a result of the classification of finite simple groups
, but no simpler proof is known.
Finite group
In mathematics and abstract algebra, a finite group is a group whose underlying set G has finitely many elements. During the twentieth century, mathematicians investigated certain aspects of the theory of finite groups in great depth, especially the local theory of finite groups, and the theory of...
, the Schreier conjecture asserts that the group of outer automorphisms of every finite simple group is 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...
. It was proposed by Otto Schreier
Otto Schreier
Otto Schreier was an Austrian mathematician who made major contributions in combinatorial group theory and in the topology of Lie groups. He studied mathematics at the University of Vienna and obtained his doctorate in 1923, under the supervision of Philipp Furtwängler...
in 1926, and is now known to be true as a result of 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...
, but no simpler proof is known.