Balance theorem

In mathematical finite group theory, the balance theorem states that if G is a group with no core then G either has disconnected Sylow 2-subgroups or it is of characteristic 2 type or it is of component type (Gorenstein & 1983 p. 7).

The significance of this theorem is that it splits the classification of finite simple groups into three major subcases.

References

• Gorenstein, D. (1983), The classification of finite simple groups. Vol. 1, The University Series in Mathematics, Plenum Press, ISBN 978-0-306-41305-6, MR 746470