| Title:
|
On multiplication groups of relatively free quasigroups isotopic to Abelian groups (English) |
| Author:
|
Drápal, Aleš |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
61-86 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
If $Q$ is a quasigroup that is free in the class of all quasigroups which are isotopic to an Abelian group, then its multiplication group $\mathop {\mathrm Mlt}Q$ is a Frobenius group. Conversely, if $\mathop {\mathrm Mlt}Q$ is a Frobenius group, $Q$ a quasigroup, then $Q$ has to be isotopic to an Abelian group. If $Q$ is, in addition, finite, then it must be a central quasigroup (a $T$-quasigroup). (English) |
| Keyword:
|
central quasigroups |
| Keyword:
|
$T$-quasigroups |
| Keyword:
|
multiplication groups |
| Keyword:
|
Frobenius groups |
| Keyword:
|
quasigroups isotopic to Abelian groups |
| MSC:
|
08B20 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1081.20078 |
| idMR:
|
MR2121656 |
| . |
| Date available:
|
2009-09-24T11:20:53Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127959 |
| . |
| Reference:
|
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| Reference:
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| . |
