Is refinement of a composition series a composition series? I was given it as an exercise to check whether every refinement of a composition series is a composition series or not?
I think it follows from the definition itself that every refinement of a composition series is a composition series.
Please correct me if I am wrong.

If you follow wikipedia's definition:

"A subnormal series is a composition series if and only if it is of maximal length. That is, there are no additional subgroups which can be "inserted" into a composition series."

So if you have a composition series you can not have a strict refinement of it i.e. every refinement is the trivial refinement so we end with the same composition series with which we started.
