| Title:
|
On Rusakov’s $n$-ary $rs$-groups (English) |
| Author:
|
Dudek, Wiesław A. |
| Author:
|
Stojaković, Zoran |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
275-283 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Properties of $n$-ary groups connected with the affine geometry are considered. Some conditions for an $n$-ary $rs$-group to be derived from a binary group are given. Necessary and sufficient conditions for an $n$-ary group $<\theta ,b>$-derived from an additive group of a field to be an $rs$-group are obtained. The existence of non-commutative $n$-ary $rs$-groups which are not derived from any group of arity $m<n$ for every $n\ge 3$, $r>2$ is proved. (English) |
| Keyword:
|
$n$-ary group |
| Keyword:
|
symmetry |
| MSC:
|
20N15 |
| MSC:
|
51A25 |
| MSC:
|
51D15 |
| idZBL:
|
Zbl 0983.20067 |
| idMR:
|
MR1844310 |
| . |
| Date available:
|
2009-09-24T10:42:22Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127647 |
| . |
| Reference:
|
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