# Balance theorem

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In **mathematical** group theory, the **balance theorem** states that if *G* is a group with no [core](/source/Core_(group)), then *G* either has disconnected [Sylow 2-subgroups](/source/Sylow_subgroup), or it is of [characteristic 2 type](/source/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](/source/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

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