title: Balance theorem
text: # Balance theorem
  
  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.
  
  