Solvability of fixed length is direct product-closed
Version in terms of fixed class bound
Version in terms of maximum class
Suppose is a collection of groups indexed by an indexing set . If all the s are solvable groups and there is a common finite bound on their derived length values, then the external direct product of the s is also a solvable group and its derived length is the maximum of the derived length values of all the s.
In particular, for two solvable groups and of derived lengths respectively, the derived length of equals .