In mathematical 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
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 0746470