Bol Loops of Order 16 with Centrum of Size 8

As part of my enumeration of the Bol loops of order 16 with nontrivial centre, here I list just the 19 loops which are non-associative with centrum of size 8. 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

• one loop with |I(L)|=7:     16.7.8.3;
• one loop with |I(L)|=9:     16.9.8.3;   and
• one loop with |I(L)|=11:     16.11.8.2.

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

• five loops with |I(L)|=3:     16.3.8.0,   16.3.8.1,   16.3.8.2,   16.3.8.3,   16.3.8.4;
• three loops with |I(L)|=7:     16.7.8.0,   16.7.8.1,   16.7.8.2;   and
• two loops with |I(L)|=11:     16.11.8.0,   16.11.8.1.

The remaining six 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 (since it has at most 10 edges), and isolated vertices are not displayed.

No.	Comm(L)	|I(L)|=5	|I(L)|=9	|I(L)|=13
2		1	1, 2	0
83		0	0

/ revised November, 2001