Abstract. Using the characterization of groups with abelian Sylow 2-subgroups, we deduce some splitting criteria. The main result is: if $G$ is a group with abelian Sylow 2-subgroups without non-trivial solvable factor groups and without non-trivial solvable normal subgroups, then any extension of $G$ splits over $G$. Also, we give new proofs of some known theorems about splitting over normal subgroups with abelian Sylow subgroups.

AMS Subject Classification (1991): 20D40, 20F17

Received March 25, 2001, and in revised form April 12, 2002. (Registered under 2861/2009.)