In mathematical group theory, the balance theorem states that if ''G'' is a group with no

core Core or cores may refer to: Science and technology * Core (anatomy), everything except the appendages * Core (manufacturing), used in casting and molding * Core (optical fiber), the signal-carrying portion of an optical fiber * Core, the centra ...

then ''G'' either has disconnected Sylow 2-subgroups or it is of

characteristic 2 type In finite group theory, a branch of mathematics, a group is said to be of characteristic 2 type or even type or of even characteristic if it resembles a group of Lie type over a field of characteristic 2. In the classification of finite simple gro ...

or it is of component type . The significance of this theorem is that it splits the

classification of finite simple groups In mathematics, the classification of the finite simple groups is a result of group theory stating that every finite simple group is either cyclic, or alternating, or it belongs to a broad infinite class called the groups of Lie type, or els ...

into three major subcases.

References

*{{Citation , last1=Gorenstein , first1=D. , author1-link=Daniel Gorenstein , title=The classification of finite simple groups. Vol. 1 , publisher=Plenum Press , series=The University Series in Mathematics , isbn=978-0-306-41305-6 , mr=746470 , year=1983 Theorems about finite groups