| Title:
|
On abelian inner mapping groups of finite loops (English) |
| Author:
|
Niemenmaa, Markku |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
687-691 |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
loop |
| Keyword:
|
group |
| Keyword:
|
connected transversals |
| MSC:
|
20D10 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1051.20034 |
| idMR:
|
MR1800173 |
| . |
| Date available:
|
2009-01-08T19:06:27Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119202 |
| . |
| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
[5] Niemenmaa M.: On the structure of the inner mapping groups of loops.Comm. Algebra 24 (1996), 135-142. Zbl 0853.20049, MR 1370527 |
| Reference:
|
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| Reference:
|
[7] Niemenmaa M., Kepka T.: On connected transversals to abelian subgroups.Bull. Austral. Math. Soc. 49 (1994), 121-128. Zbl 0799.20020, MR 1262682 |
| Reference:
|
[8] Rotman J.: An introduction to the theory of groups.Springer-Verlag, 1995. Zbl 0810.20001, MR 1307623 |
| Reference:
|
[9] Vesanen A.: On connected transversals in $PSL(2,q)$.Ann. Acad. Sci. Fenn., Series A, I. Mathematica, Dissertationes 84, 1992. Zbl 0744.20058, MR 2714539 |
| Reference:
|
[10] Vesanen A.: The group $PSL(2,q)$ is not the multiplication group of a loop.Comm. Algebra 22 (1994), 1177-1195. MR 1261254 |
| . |
