Bol Loops of Order 16 with 11 Involutions

As part of my enumeration of the Bol loops of order 16 with nontrivial centre, here I list just the 316 loops which are non-associative with exactly eleven 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 six loops in this category have |Z(L)|=4, namely

The remaining 307 loops 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
3 263    
7 111, 130, 214    
8 62, 89, 159    
11 14, 26, 226    
14   12, 19  
17 250, 262    
20 3, 4, 5, 8, 9, 249, 265    
24 43, 213    
25   9, 11, 30  
28 77, 139, 231    
30 237, 243, 252    
31 58, 121    
34   26  
39 47, 54, 119    
45   7, 39  
48 97, 242, 253    
49   4  
50   20, 27, 28  
53 61, 266    
54 142, 205    
56 88, 153, 201    
59 131, 186, 199    
61 98, 128, 251    
62 113, 120, 152    
64 124, 244    
66 151, 211, 247    
68 15, 25, 51    
72 117, 127, 192    
74 182, 197, 207    
75 126, 134, 137    
77 140, 169, 191    
82 154, 176, 185, 190, 196, 210, 238    
84   13, 18  
87 79, 82, 155, 162, 187, 189    
88 92, 217, 228    
90 74, 106, 204    
92 75, 103, 261    
95 254, 267    
98 17, 19, 188    
100   8, 10, 15, 17, 31, 35  
105 102, 148, 224    
107 174, 233, 234    
109 195, 202, 246    
111 21, 23, 115    
112 65, 112, 216    
115 37, 264    
117 163, 184, 230    
119 87, 255    
120   14, 16, 36  
122 96, 158, 177    
125 40, 64    
127 44, 222    
129 136, 178, 179    
132 35, 39, 116    
136 135, 150, 180    
138 109, 183, 245    
139 84, 193, 218    
141 78, 110, 240    
143   23, 37  
146 138, 146, 165, 215, 239    
152 0, 6    
156 1, 2, 7    
157 57, 198    
159 95, 181, 227    
161   21, 33  
163 16, 24, 175    
165   24, 38  
167 31, 53    
169 28, 66, 80    
172 63, 72, 86    
174 18, 22, 149    
177 171, 194    
179 122, 144, 236    
182 49, 52, 143    
184 101, 125, 160    
185 11, 12, 20, 33, 108, 168    
187 10, 13, 46, 59, 60, 235    
193 100, 167, 173    
195 27, 30, 36, 38, 93, 157    
200 68, 170, 241    
202 129, 232    
204 76, 94, 141    
206 32, 48, 225    
208 55, 229    
210 29, 56, 223    
212     0, 1, 2, 3
215 69, 221, 258    
216 71, 208, 212    
218   5  
219   22, 25, 32  
222 105    
224 147, 161, 259    
225   29, 34  
227 42, 45, 50    
230 85, 107, 257    
232 91, 256    
233 83, 90, 209    
235 67, 156, 248    
237 99, 118, 203    
239 132, 172, 220    
241 34, 41, 200    
246 70, 73, 114, 145, 166, 219    
248 123    
249 81, 133, 260    
251 104, 164, 206    

/ revised November, 2001