Total anti-symmetrische Quasigruppen
Bei der Untersuchung von Prüfziffersystemen über Quasigruppen stößt man auf die so genannten total anti-symmetrischen Quasigruppen. Bislang war ihre Existenz für alle Ordnungen $4k+2\geq 10$ ungeklärt. Ecker und Poch vermuteten 1986, dass es keine total anti-symmetrischen Quasigruppen der Ordnung $4...
Prif Awdur: | |
---|---|
Awduron Eraill: | |
Fformat: | Dissertation |
Iaith: | Almaeneg |
Cyhoeddwyd: |
Philipps-Universität Marburg
2004
|
Pynciau: | |
Mynediad Ar-lein: | Testun PDF llawn |
Tagiau: |
Ychwanegu Tag
Dim Tagiau, Byddwch y cyntaf i dagio'r cofnod hwn!
|
Totally anti-symmetric quasigroups are employed in check digit systems. Until today their existence for all orders $4k+2\geq 10$ was unsettled. Ecker and Poch conjectured in 1986 that there are no totally anti-symmetric quasigroups of order $4k+2$. We disprove this conjecture and develop constructions for totally anti-symmetric quasigroups of order $n$ for all $n\neq 2,6$. By a computer search we prove in addition that check digit systems over a 2-quasigroup of the order 10, just as check digit systems over groups of order 10, cannot detect all (jump) twin errors or jump transpositions. As a further result we show that the class of totally anti-symmetric quasigroups is no variety.