Composition length of direct product is sum of composition lengths
This article gives an expression for the value of the arithmetic function composition length of an external direct product in terms of the values for the direct factors. It says that the value for the direct product is the sum of the values for the direct factors.
View facts about composition length: (facts closely related to composition length, all facts related to composition length)
View facts about external direct product: (facts closely related to external direct product, all facts related to external direct product)
View facts about sum: (facts closely related to sum, all facts related to sum)
For two groups
In particular, if both and are groups of finite composition length, then so is . Conversely, if is a group of finite composition length, then so are and .