| Title:
|
Extending the structural homomorphism of LCC loops (English) |
| Author:
|
Csörgö, Piroska |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
385-389 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A loop $Q$ is said to be left conjugacy closed if the set $A=\{L_x/x\in Q\}$ is closed under conjugation. Let $Q$ be an LCC loop, let $\Cal L$ and $\Cal R$ be the left and right multiplication groups of $Q$ respectively, and let $I(Q)$ be its inner mapping group, $M(Q)$ its multiplication group. By Drápal's theorem [3, Theorem 2.8] there exists a homomorphism $\Lambda : \Cal L \to I(Q)$ determined by $L_x\to R^{-1}_x L_x$. In this short note we examine different possible extensions of this $\Lambda$ and the uniqueness of these extensions. (English) |
| Keyword:
|
LCC loop |
| Keyword:
|
multiplication group |
| Keyword:
|
inner mapping group |
| Keyword:
|
homomorphism |
| MSC:
|
20D10 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1106.20051 |
| idMR:
|
MR2174517 |
| . |
| Date available:
|
2009-05-05T16:51:47Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119533 |
| . |
| Reference:
|
[1] Basarab A.S.: A class of LK-loops (in Russian).Mat. Issled. 120 (1991), 3-7. MR 1121425 |
| Reference:
|
[2] Drápal A.: Conjugacy closed loops and their multiplication groups.J. Algebra 272 (2004), 838-850. Zbl 1047.20049, MR 2028083 |
| Reference:
|
[3] Drápal A.: On multiplication groups of left conjugacy closed loops.Comment. Math. Univ. Carolinae 45 (2004), 223-236. Zbl 1101.20035, MR 2075271 |
| Reference:
|
[4] Goodaire E.G., Robinson D.A.: A class of loops which are isomorphic to all loop isotopes.Canad. J. Math. 34 (1982), 662-672. Zbl 0467.20052, MR 0663308 |
| Reference:
|
[5] Kiechle H., Nagy G.P.: On the extension of involutorial Bol loops.Abh. Math. Sem. Univ. Hamburg 72 (2002), 235-250. Zbl 1016.20051, MR 1941556 |
| Reference:
|
[6] Nagy P., Strambach K.: Loops as invariant sections in groups and their geometry.Canad. J. Math. 46 (1994), 1027-1056. Zbl 0814.20055, MR 1295130 |
| Reference:
|
[7] Soikis L.R.: The special loops (in Russian).in: Voprosy teorii kvazigrupp i lup (V.D. Belousov, ed.), Akademia Nauk Moldav. SSR, Kishinyev, 1970, pp.122-131. MR 0281828 |
| . |
