On transitive commutative idempotent quasigroups

Arnold Neumaier
1979 Journal of the Australian Mathematical Society  
Commutative idempotent quasigroups with a sharply transitive automorphism group G are described in terms of so-called Room maps of G. Orthogonal Room maps and skew Room maps are used to construct Room squares and skew Room squares. Very general direct and recursive constructions for skew Room maps lead to the existence of skew Room maps of groups of order prime to 30. Also some nonexistence results are proved. 1980 Mathematics subject classification (Amer. Math. Soc.): primary 05 B 15;
more » ... y 05 B 15; secondary 20 N 05.
doi:10.1017/s1446788700013422 fatcat:sljcxdevp5apxnpqvoxfmksdj4