| Title:
|
On the structure of finite loop capable Abelian groups (English) |
| Author:
|
Niemenmaa, Markku |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
48 |
| Issue:
|
2 |
| Year:
|
2007 |
| Pages:
|
217-224 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Loop capable groups are groups which are isomorphic to inner mapping groups of loops. In this paper we show that abelian groups $C_p^{k}\times C_p\times C_p$, where $k\geq 2$ and $p$ is an odd prime, are not loop capable groups. We also discuss generalizations of this result. (English) |
| Keyword:
|
loop |
| Keyword:
|
group |
| Keyword:
|
connected transversals |
| MSC:
|
20D10 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1174.20345 |
| idMR:
|
MR2338090 |
| . |
| Date available:
|
2009-05-05T17:02:26Z |
| Last updated:
|
2012-05-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119652 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] Niemenmaa M.: On finite loops whose inner mapping groups are abelian.Bull. Austral. Math. Soc. 65 (2002), 477-484. Zbl 1012.20068, MR 1910500 |
| Reference:
|
[9] Niemenmaa M.: On finite loops whose inner mapping groups are abelian II.Bull. Austral. Math. Soc. 71 (2005), 487-492. Zbl 1080.20061, MR 2150938 |
| Reference:
|
[10] Niemenmaa M., Kepka T.: On connected transversals to abelian subgroups.Bull. Austral. Math. Soc. 49 (1994), 121-128. Zbl 0799.20020, MR 1262682 |
| . |
