| Title:
|
On multiplication groups of left conjugacy closed loops (English) |
| Author:
|
Drápal, Aleš |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
2 |
| Year:
|
2004 |
| Pages:
|
223-236 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A loop $Q$ is said to be left conjugacy closed (LCC) if the set $\{L_x; x \in Q\}$ is closed under conjugation. Let $Q$ be such a loop, let $\Cal L$ and $\Cal R$ be the left and right multiplication groups of $Q$, respectively, and let $\operatorname{Inn} Q$ be its inner mapping group. Then there exists a homomorphism $\Cal L \to \operatorname{Inn} Q$ determined by $L_x \mapsto R^{-1}_xL_x$, and the orbits of $[\Cal L, \Cal R]$ coincide with the cosets of $A(Q)$, the associator subloop of $Q$. All LCC loops of prime order are abelian groups. (English) |
| Keyword:
|
left conjugacy closed loop |
| Keyword:
|
multiplication group |
| Keyword:
|
nucleus |
| MSC:
|
08A05 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1101.20035 |
| idMR:
|
MR2075271 |
| . |
| Date available:
|
2009-05-05T16:44:41Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119452 |
| . |
| Reference:
|
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