algebra group; quasigroup; loop; supercharacter; fusion scheme
A natural loop structure is defined on the set $U_4$ of unimodular upper-triangular matrices over a given field. Inner mappings of the loop are computed. It is shown that the loop is non-associative and nilpotent, of class 3. A detailed listing of the loop conjugacy classes is presented. In particular, one of the loop conjugacy classes is shown to be properly contained in a superclass of the corresponding algebra group.
 Smith J.D.H.: An Introduction to Quasigroups and Their Representations
. Chapman and Hall/CRC, Boca Raton, FL, 2007. MR 2268350
| Zbl 1122.20035