Bol Loops of Order 20

I've been working on a classification of Bol loops of small order. Here is a list of the 8 Bol loops of order 20. This includes the five 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

a quick review of the relevant definitions;
a suitable list of references for further explanation, proofs, etc.;
a cross-reference list comparing this list with previously published lists of groups and loops;
descriptions of these loops in html format, found through the links below; and
the Cayley tables (8 KB) in plain text form.

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 20.)

The 8 Bol Loops

The Five Groups: 20.1.20.0, 20.1.2.0, 20.3.20.0, 20.11.2.0, 20.5.1.0

The non-associative Moufang Loop: 20.15.1.1

The non-Moufang (non-associative) Bol Loops: 20.7.3.0, 20.15.1.0

Naming of the Loops

For each of the loops of order 20, I have used a name 20.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