| Title:
|
On a class of commutative groupoids determined by their associativity triples (English) |
| Author:
|
Drápal, Aleš |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
2 |
| Year:
|
1993 |
| Pages:
|
199-201 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G = G(\cdot)$ be a commutative groupoid such that $\{(a,b,c) \in G^3$; $a\cdot bc \ne ab\cdot c\} = \{(a,b,c) \in G^3$; $a=b\ne c$ or $ a \ne b =c \}$. Then $G$ is determined uniquely up to isomorphism and if it is finite, then $\operatorname{card}(G) = 2^i$ for an integer $i\ge 0$. (English) |
| Keyword:
|
commutative groupoid |
| Keyword:
|
associative triples |
| MSC:
|
05B15 |
| MSC:
|
05E99 |
| MSC:
|
20L05 |
| MSC:
|
20N02 |
| idZBL:
|
Zbl 0787.20040 |
| idMR:
|
MR1241727 |
| . |
| Date available:
|
2009-01-08T18:02:28Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118571 |
| . |
| Reference:
|
[1] Drápal A., Kepka T.: Sets of associative triples.Europ. J. Combinatorics 6 (1985), 227-231. MR 0818596 |
| Reference:
|
[2] Drápal A.: Groupoids with non-associative triples on the diagonal.Czech. Math. Journal 35 (1985), 555-564. MR 0809042 |
| . |
