Varieties of quasigroups arising from 2-perfectm-cycle systems

✍ Scribed by Darryn E. Bryant

• Publisher: Springer
• Year: 1992
• Tongue: English
• Weight: 480 KB
• Volume: 2
• Category: Article
• ISSN: 0925-1022
• DOI: 10.1007/bf00124894

✦ Synopsis

For m = 6 and for all odd composite integers m, as well as for all even integers m > 10 that satisfy certain conditions, 2-poffect m-cycle systems are constructed whose quasigroups have a homomorphism onto qnasigroups which do not correspond to a 2-perfect m-cycle systems. Thus it is shown that for these values of m the class of quasigroups arising from all 2-perfect m-cycle systems does not form a variety.