Bol Loops of Order 16 with 3 Involutions

As part of my enumeration of the Bol loops of order 16 with nontrivial centre, here I list just the 157 loops which are non-associative with exactly three 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.

21 loops were found in this category with |Z(L)|=4, namely

The remaining 136 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
3 106    
7 103    
8 47    
11 28    
14   37  
17 104    
20 105, 108, 110    
24 70    
25   36  
28 77    
30 96    
31 65    
34   39  
36 2, 3, 4, 5    
37 8, 111    
39 50    
41 9    
45   10, 11, 26  
48 88    
49   20  
50   31  
53 84    
54 101    
56 62    
59 97    
61 54    
62 16    
64 61    
66 27    
68 56    
72 33    
74 57    
75 45    
77 18    
82 82, 83, 95    
84   33  
87 69, 75    
88 23    
90 85    
92 99    
95 100    
98 53    
100   28, 29  
105 37    
107 11    
109 38    
111 15    
112 48    
115 73    
117 52    
119 67    
120   34  
122 14    
124 10    
125 89    
127 43    
129 46    
132 29    
136 76    
138 31    
139 40    
141 49    
143   27  
146 12, 98    
147   8, 9  
149   18, 40  
150 0, 1, 6, 7    
152 107    
156 109    
157 92    
159 26    
161   38  
163 25    
165   35  
167 74    
169 78    
172 79    
174 36    
177 55    
179 93    
182 30    
184 44    
185 80, 87    
187 13, 59    
193 35    
195 39, 51    
200 21    
202 94    
204 58    
206 32    
208 63    
210 41    
212     0, 1
215 60    
216 34    
218   19  
219   32  
222 19    
224 91, 102    
225   30  
227 86    
230 64    
232 72    
233 42    
235 90    
237 68    
239 17    
241 22    
246 20, 24    
248 66    
249 81    
251 71    

/ revised November, 2001