A new condition for solvable groups.

A subgroup H of G is called complemented in G if there exists a subgroup K of G such that G = H K and H ∩ K = 1 . The aim of this paper is to prove the following: A finite group G is solvable if and only if its Sylow 3-, 5- and 7-subgroups are complemented in G . [ABSTRACT FROM AUTHOR]