| Title:
|
A class of Bol loops with a subgroup of index two (English) |
| Author:
|
Vojtěchovský, Petr |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
2 |
| Year:
|
2004 |
| Pages:
|
371-381 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be a finite group and $C_2$ the cyclic group of order $2$. Consider the $8$ multiplicative operations $(x,y)\mapsto (x^iy^j)^k$, where $i$, $j$, $k\in\{-1,\,1\}$. Define a new multiplication on $G\times C_2$ by assigning one of the above $8$ multiplications to each quarter $(G\times\{i\})\times(G\times\{j\})$, for $i, j\in C_2$. We describe all situations in which the resulting quasigroup is a Bol loop. This paper also corrects an error in P. Vojt\v{e}chovsk'y: On the uniqueness of loops $M(G,2)$. (English) |
| Keyword:
|
Moufang loops |
| Keyword:
|
loops $M(G, 2)$ |
| Keyword:
|
inverse property loops |
| Keyword:
|
Bol loops |
| MSC:
|
20A05 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1101.20048 |
| idMR:
|
MR2075284 |
| . |
| Date available:
|
2009-05-05T16:45:51Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119465 |
| . |
| 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:
|
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| . |
