I'm kind of stuck in this problem on my Algebra study.
I have to prove that given $(L,\leq)$ a modular lattice, $a,b,c \in L$ such that $a \leq b \leq c$, the interval $[a,c]$ admits a composition series if and only if the intervals $[a,b]$ and $[b,c]$ admit a composition series respectively and also that $l[a,c]=l[a,b]+l[b,c]$.
Of course I've proven the part of composition series, but I'm kind of confused with that " $l$ ". I think it means $length$, but I can't find any information about it.
Any help is welcome!