Bol Loops of Order 28

I've been working on a classification of Bol loops of small order. Here is a list of the 7 Bol loops of order 28. This includes the four groups, one non-associative Moufang loop, and two non-Moufang (and non-associative) Bol loops. The latter two examples are isotopic, but the other six are G-loops. The completeness of this list follows from Burn (1981).

I have made available

In listing elements of the commutator (resp. associator) subloop of each of these loops, we have printed in italics any elements which are not actual commutators (resp. associators). (I have not checked whether this phenomenon occurs in any of the loop of order 28.)

The 7 Bol Loops

The four Groups:,,,

The non-associative Moufang Loop:

The two non-Moufang (non-associative) Bol Loops:,

Naming of the Loops

For each of the loops of order 28, I have used a name 28.i.c.k where i is the number of involutions, c=|C(L)| and the index k=0,1,2,... indicates merely the order in which each isomorphism class of loop was first encountered by my computer.

/ revised February, 2005