Bol Loops of Order 16 with 5 Involutions

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

All 338 loops in this list 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 |C(L)|=8
2       1
6   19, 23, 24    
9 73, 230, 260      
10 6, 7, 286      
12 151, 256, 269      
13 9, 287      
15 163, 280      
16 63, 187      
18 14, 15, 16      
19 86, 113      
23 90, 150      
26 199, 217, 222      
27 160, 176, 219      
29 19, 91, 109      
32 121, 283      
33 1, 4, 8, 285      
35 111      
38   2, 3, 4, 5, 14    
40 123, 180, 200      
43 12, 13      
44 74, 106, 279      
46 282, 284      
47 88, 122, 175      
51 49, 102, 228      
52 87, 147      
55 262, 271      
57 64, 127, 129      
58   17, 21, 40    
60   33, 35, 41    
63 80, 164, 244      
65 110, 239      
67 213, 226, 249      
69 33, 211, 261      
70 11, 289      
71 46, 158, 161      
73 18, 41, 145      
76 198, 241, 265      
78 131, 134, 185      
81 66, 71, 89, 115, 140, 149, 156      
83       0
85 238, 278      
86   15, 20, 25, 29, 32, 38    
89 159, 167, 196      
91 92, 93, 100      
93 98, 190, 275      
94   10, 16, 31, 44    
99 40, 79, 105      
101 51, 171, 197, 246, 266, 281      
104 44, 169, 186      
106 42, 83, 96      
108 38, 153, 221      
110 48, 136, 181      
113 133, 141, 179      
114     0, 1  
116 132, 154, 258      
118 50, 144      
121 124, 157, 232      
123 22, 117, 120      
126 78, 253      
128 58, 182      
130 174, 203, 268      
131 139, 208, 227      
135 57, 135, 148      
137 36, 53, 76      
140 52, 62, 81      
142 56, 84, 95      
144 65, 85      
145 20, 21, 94, 146, 254      
147   8, 9    
149   0, 1, 6, 7, 12    
158 243, 272      
160 34, 104, 143      
162 125, 236      
164 37, 142, 168      
166 173, 245      
168   11, 37, 42, 43    
170 82, 101, 162      
171 0, 2, 3, 5      
173 177, 194, 223      
175 39, 112, 229      
176   26, 36    
178 10, 288      
180 235, 237, 264      
181 107, 193, 205      
183 60, 61, 242      
186 31, 47, 54, 114, 231, 252      
188 28, 155, 166, 170, 191, 201      
194 70, 247, 259      
196 67, 99, 103, 138, 250, 251      
199 188, 210, 233      
201 25, 59      
203   13    
205 68, 165, 189      
207 30, 75, 195      
209 45, 212      
211 108, 137, 216      
213 55, 97, 276, 277      
214   18, 22, 28    
217 72, 128, 183      
220 202, 204, 215      
221   30    
223 23, 26, 218      
226 267, 270      
228 152, 192, 224      
229 116, 118, 220      
231 24, 35      
234 69, 206, 207      
236   27, 34, 39    
238 178, 248, 255      
240 43, 126, 214      
242 184, 240, 273      
245 27, 29, 32, 77, 225, 234      
247 257      
250 119, 130, 172      
252 209, 263, 274      

/ revised November, 2001