A loop transversal in a sharply 2-transitive permutation loop

Eugene Kuznetsov

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chişinău, Moldova

Abstract: The well-known theorem of M. Hall about the description of a finite sharply 2-transitive permutation group is generalized for the case of permutation loops. It is shown that the identity permutation with the set of all fixed-point-free permutations in a finite sharply 2-transitive permutation loop forms a loop transversal by its proper subloop – a stabilizator of one symbol.

Keywords and phrases: Quasigroup, loop, transversal, projective plane.

MSC: 20N05

Received: 22.08.2005

Language: English

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