Search: MSC category 05B07
( Triple systems )
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||Distributive and anti-distributive Mendelsohn triple systems|
We prove that the existence spectrum of Mendelsohn triple systems
whose associated quasigroups satisfy distributivity corresponds
to the Loeschian numbers, and provide some enumeration results.
We do this by considering a description of the quasigroups in
terms of commutative Moufang loops.
In addition we provide constructions of Mendelsohn quasigroups
that fail distributivity for as many combinations of elements
These systems are analogues of Hall triple systems and anti-mitre
Steiner triple systems respectively.
Keywords:Mendelsohn triple system, quasigroup, distributive, Moufang loop, Loeschian numbers