| Title:
|
On finite loops whose inner mapping groups have small orders (English) |
| Author:
|
Niemenmaa, Markku |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
3 |
| Year:
|
1996 |
| Pages:
|
651-654 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
solvability |
| Keyword:
|
loop |
| Keyword:
|
group |
| MSC:
|
20B25 |
| MSC:
|
20D10 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 0881.20006 |
| idMR:
|
MR1426930 |
| . |
| Date available:
|
2009-01-08T18:26:56Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118872 |
| . |
| Reference:
|
[1] Blackburn N., Huppert B.: Finite Groups III.Springer Verlag, 1982. Zbl 0514.20002, MR 0662826 |
| Reference:
|
[2] Conway J.H.: Atlas of Finite Groups.Oxford, Clarendon Press, 1985. Zbl 0568.20001, MR 0827219 |
| Reference:
|
[3] Huppert B.: Endliche Gruppen I.Springer Verlag, 1967. Zbl 0412.20002, MR 0224703 |
| Reference:
|
[4] Kepka T., Niemenmaa M.: On loops with cyclic inner mapping groups.Arch. Math. 60 (1993), 233-236. MR 1201636 |
| Reference:
|
[5] Niemenmaa M.: Transversals, commutators and solvability in finite groups.Bollettino U.M.I. (7) 9-A (1995), 203-208. Zbl 0837.20026, MR 1324621 |
| Reference:
|
[6] Niemenmaa M., Kepka T.: On multiplication groups of loops.J. Algebra 135 (1990), 112-122. Zbl 0706.20046, MR 1076080 |
| Reference:
|
[7] Niemenmaa M., Kepka T.: On connected transversals to abelian subgroups in finite groups.Bull. London Math. Soc. 24 (1992), 343-346. Zbl 0793.20064, MR 1165376 |
| Reference:
|
[8] Niemenmaa M., Vesanen A.: On subgroups, transversals and commutators.Groups Galway/St. Andrews, 1993, Vol.2, London Math. Soc. Lecture Notes Series 212, 1995, pp. 476-481. Zbl 0862.20023, MR 1337289 |
| Reference:
|
[9] Vesanen A.: On connected transversals in $PSL(2,q)$.Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes 84, 1992. Zbl 0744.20058, MR 1150782 |
| Reference:
|
[10] Vesanen A.: The group $PSL(2,q)$ is not the multiplication group of a loop.Comm. Algebra 22.4 (1994), 1177-1195. MR 1261254 |
| Reference:
|
[11] Vesanen A.: Solvable loops and groups.to appear in J. Algebra. MR 1379214 |
| . |
