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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

Mathematics Encyclopedia