| Title:
|
On the structure of finite loop capable nilpotent groups (English) |
| Author:
|
Rytty, Miikka |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
349-355 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we consider finite loops and discuss the problem which nilpotent groups are isomorphic to the inner mapping group of a loop. We recall some earlier results and by using connected transversals we transform the problem into a group theoretical one. We will get some new answers as we show that a nilpotent group having either $C_{p^k} \times C_{p^l}$, $k > l \geq 0$ as the Sylow $p$-subgroup for some odd prime $p$ or the group of quaternions as the Sylow $2$-subgroup may not be loop capable. (English) |
| Keyword:
|
loop |
| Keyword:
|
group |
| Keyword:
|
connected transversals |
| MSC:
|
20D10 |
| MSC:
|
20D15 |
| MSC:
|
20F18 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1211.20021 |
| idMR:
|
MR2682486 |
| . |
| Date available:
|
2010-05-21T12:53:35Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140112 |
| . |
| 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:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
[12] Niemenmaa M.: Finite loops with nilpotent inner mapping groups are centrally nilpotent.Bull. Aust. Math. Soc. 79 (2009), 109–114. Zbl 1167.20039, MR 2486887, 10.1017/S0004972708001093 |
| . |
