) from you if you have any comments regarding this list.
As part of my enumeration of Bol loops of order 16
with nontrivial centre,
here I list just the 33 loops which are non-associative with exactly fifteen involutions.
Please see the parent page for notation, including
my conventions for naming of loops and table entries.
I would appreciate an email
message () from you if you have any comments regarding this list.
Three loops in this category have |Z(L)|=1, namely
Also two loops in this category have |Z(L)|=4, both with |C(L)|=4, namely 16.15.4.0 and 16.15.4.1.
The remaining 28 loops found in this category all have |Z(L)|=2 and so the graph Comm(L) is defined. This graph is displayed as black-on-white if it has at most 10 edges; otherwise its complement (which has at most 10 edges) is displayed as white-on-black. In either case, isolated vertices are not displayed.
| No. | Comm(L) | |C(L)|=2 | |C(L)|=4 | |C(L)|=6 |
|---|---|---|---|---|
| 4 | 
| 0 | ||
| 11 | 
| 4 | ||
| 20 | 
| 2, 3 | ||
| 22 | 
| 17 | ||
| 43 | 
| 20 | ||
| 50 | 
| 3 | ||
| 61 | 
| 22 | ||
| 68 | 
| 6 | ||
| 80 | 
| 14 | ||
| 96 | 
| 9 | ||
| 103 | 
| 18 | ||
| 134 | 
| 12 | ||
| 152 | 
| 0, 23 | ||
| 154 | 
| 10 | ||
| 156 | 
| 1, 21 | ||
| 185 | 
| 5 | ||
| 187 | 
| 7 | ||
| 189 | 
| 4 | ||
| 191 | 
| 11 | ||
| 197 | 
| 15 | ||
| 219 | 
| 2 | ||
| 222 | 
| 13 | ||
| 227 | 
| 8 | ||
| 235 | 
| 19 | ||
| 244 | 
| 16 |
/
revised November, 2001