论文信息 - Multiplication Groups of Loops and Projective Semilinear Transformations in Dimension Two

Multiplication Groups of Loops and Projective Semilinear Transformations in Dimension Two

Abstract For a loop Q denote by Mlt Q the permutation group generated by translations x ↦ xa and x ↦ ax , a ∈ Q . If Q is defined on F ∪ {∞}, where F is a finite field with at least five elements, and if Mlt Q ≤ PΓL (2, F ), then Q is an abelian group. The same result holds for an infinite field F , if the automorphisms associated with translations generate a finite subgroup of Aut( F ).

Aleš Drápal | A. Drápal

[1] The group PSL(2,q) is not the multiplication group of a loop , 1994 .

[2] N. J. A. Sloane,et al. Sphere Packings, Lattices and Groups , 1987, Grundlehren der mathematischen Wissenschaften.

[3] W. Burnside,et al. Theory of Groups of Finite Order , 1909 .

[4] T. Kepka,et al. On multiplication groups of loops , 1990 .

[5] Ales Drápal,et al. Alternating Groups and Latin Squares , 1989, Eur. J. Comb..

[6] Aleš Drápal,et al. Multiplication Groups of Finite Loops That Fix at Most Two Points , 2001 .