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Collineation groups of the smallest Bol 3-nets

Gabor P. Nagy
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Abstract

Some associativity properties of a loop can be interpreted as certain closure configuration of the corresponding 3-net. It was known that the smallest non-associative loops with the so called left Bol property have order 8. In this paper, we determine the direction preserving collineation groups of the 3-nets belonging to these smallest Bol loops. For that, we prove some new results concerning collineations of 3-nets and autotopisms of loops.

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Gabor P. Nagy. 2004-11-14. Collineation groups of the smallest Bol 3-nets. https://arxiv.org/abs/math/0411317

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