| Title:
|
On centrally nilpotent loops (English) |
| Author:
|
Safonova, L. V. |
| Author:
|
Shchukin, K. K. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
2 |
| Year:
|
2000 |
| Pages:
|
401-404 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Using a lemma on subnormal subgroups, the problem of nilpotency of multiplication groups and inner permutation groups of centrally nilpotent loops is discussed. (English) |
| Keyword:
|
group |
| Keyword:
|
subnormal subgroup |
| Keyword:
|
loop |
| Keyword:
|
multiplication group |
| Keyword:
|
inner permutation group |
| MSC:
|
20B35 |
| MSC:
|
20N05 |
| MSC:
|
22A30 |
| MSC:
|
53A60 |
| MSC:
|
53C05 |
| MSC:
|
53C22 |
| MSC:
|
53C35 |
| idZBL:
|
Zbl 1038.20052 |
| idMR:
|
MR1780880 |
| . |
| Date available:
|
2009-01-08T19:02:36Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119172 |
| . |
| Reference:
|
[1] Baer R.: Abzählbar erkennbare gruppentheoretische Eigenschaften.Math. Z. 79 (1962), 344-363. Zbl 0105.25901, MR 0148740 |
| Reference:
|
[2] Safonova L.V., Shchukin K.K.: About n-Engel elements of groups.12-th Algebr. Coll. of USSR, Thesis-book 1 Sverdlovsk (1973), 54. |
| Reference:
|
[3] Smith J.D.: Multiplication groups of quasigroups.Preprint 603, Technische Hochschule Darmstadt (1981). |
| Reference:
|
[4] Bruck R.H.: A Survey of Binary Systems.Springer-Verlag (1966). Zbl 0141.01401, MR 0093552 |
| Reference:
|
[5] Shchukin K.K.: On nilpotency of the multiplication group of an $A$-loop.Mat. Issled. 162 (1988), 116-117. Zbl 0664.20043, MR 0947466 |
| Reference:
|
[6] Macdonald D., Neumann B.H.: A third-Engel 5-group.J. Austral. Math. Soc. 7 (1967), 555-569. Zbl 0163.02502, MR 0222171 |
| . |
