We investigate the situation that the inner mapping group of a loop is of order which is a product of two small prime numbers and we show that then the loop is soluble.
@article{118872, author = {Markku Niemenmaa}, title = {On finite loops whose inner mapping groups have small orders}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {37}, year = {1996}, pages = {651-654}, zbl = {0881.20006}, mrnumber = {1426930}, language = {en}, url = {http://dml.mathdoc.fr/item/118872} }
Niemenmaa, Markku. On finite loops whose inner mapping groups have small orders. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) pp. 651-654. http://gdmltest.u-ga.fr/item/118872/
Finite Groups III, Springer Verlag, 1982. | MR 0662826 | Zbl 0514.20002
Atlas of Finite Groups, Oxford, Clarendon Press, 1985. | MR 0827219 | Zbl 0568.20001
Endliche Gruppen I, Springer Verlag, 1967. | MR 0224703 | Zbl 0412.20002
On loops with cyclic inner mapping groups, Arch. Math. 60 (1993), 233-236. (1993) | MR 1201636
Transversals, commutators and solvability in finite groups, Bollettino U.M.I. (7) 9-A (1995), 203-208. (1995) | MR 1324621 | Zbl 0837.20026
On multiplication groups of loops, J. Algebra 135 (1990), 112-122. (1990) | MR 1076080 | Zbl 0706.20046
On connected transversals to abelian subgroups in finite groups, Bull. London Math. Soc. 24 (1992), 343-346. (1992) | MR 1165376 | Zbl 0793.20064
On subgroups, transversals and commutators, Groups Galway/St. Andrews, 1993, Vol.2, London Math. Soc. Lecture Notes Series 212, 1995, pp. 476-481. | MR 1337289 | Zbl 0862.20023
On connected transversals in $PSL(2,q)$, Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes 84, 1992. | MR 1150782 | Zbl 0744.20058
The group $PSL(2,q)$ is not the multiplication group of a loop, Comm. Algebra 22.4 (1994), 1177-1195. (1994) | MR 1261254
Solvable loops and groups, to appear in J. Algebra. | MR 1379214