loop; subloop; chain; uniserial
All ordinal numbers $\alpha$ with the following property are found: there exists a loop such that its subloops form a chain of ordinal type $\alpha$.
 Smith J.D.H.: An Introduction to Quasigroups and their Representations
. CRC Press, Boca Raton, FL, 2007. MR 2268350
| Zbl 1122.20035