Article
Full entry |
PDF
(0.1 MB)
Feedback
PDF
(0.1 MB)
Feedback
Keywords:
loop; group; connected transversals
loop; group; connected transversals
Summary:
In this paper we consider finite loops of specific order and we show that certain abelian groups are not isomorphic to inner mapping groups of these loops. By using our results we are able to construct a finite solvable group of order 120 which is not isomorphic to the multiplication group of a finite loop.
References:
[1] Denes J., Keedwell A.D.: Latin squares and their applications. Akademiai Kiado, Budapest, 1974. MR 0351850 | Zbl 0283.05014
[2] Drápal A., Kepka T.: Alternating groups and latin squares. European J. Combin. 10 (1989), 175-180. MR 0988511
[3] Kepka T., Niemenmaa M.: On loops with cyclic inner mapping groups. Arch. Math. 60 (1993), 233-236. MR 1201636
[4] Liebeck M.: The classification of the finite simple Moufang loops. Math. Proc. Camb. Phil. Soc. 102 (1987), 33-47. MR 0886433
[5] Niemenmaa M.: On the structure of the inner mapping groups of loops. Comm. Algebra 24 (1996), 135-142. MR 1370527 | Zbl 0853.20049
[6] Niemenmaa M., Kepka T.: On multiplication groups of loops. J. Algebra 135 (1990), 112-122. MR 1076080 | Zbl 0706.20046
[7] Niemenmaa M., Kepka T.: On connected transversals to abelian subgroups. Bull. Austral. Math. Soc. 49 (1994), 121-128. MR 1262682 | Zbl 0799.20020
[8] Rotman J.: An introduction to the theory of groups. Springer-Verlag, 1995. MR 1307623 | Zbl 0810.20001
[9] Vesanen A.: On connected transversals in $PSL(2,q)$. Ann. Acad. Sci. Fenn., Series A, I. Mathematica, Dissertationes 84, 1992. MR 2714539 | Zbl 0744.20058
[10] Vesanen A.: The group $PSL(2,q)$ is not the multiplication group of a loop. Comm. Algebra 22 (1994), 1177-1195. MR 1261254
Search
Partner of
