Quasigroups and tactical systems
โ Scribed by Ronald D. Baker
- Publisher
- Springer
- Year
- 1978
- Tongue
- English
- Weight
- 354 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0001-9054
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
A recent result of Bryant and Lindner shows that the quasigroups arising from 2-perfect m-cycle systems form a variety only when m = 3, 5 and 7. Here we investigate the situation in the case where the distance two cycles are required to be in the original system.
In this paper, we show that any partial extended triple system (partial totally symmetric quasigroup) of order n can be embedded in a totally symmetric quasigroup of order v, v >~4n +6, v -= 2(mod4). This bound can be lowered to 4n + 2 in most cases.
Two connexions between quasigroups and quandles are established. In one direction, Joyce's homogeneous quandle construction is shown to yield a quasigroup isotopic to the loop constructed by Scimemi on the set of @-commutators of a group automorphism @ In the other direction, the universal multiplic