Geodesic
On multiplication groups of left conjugacy closed loops
Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 2, pp. 223-236 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 08A05, 20N05
Keywords: left conjugacy closed loop; multiplication group; nucleus 
@article{CMUC_2004_45_2_a3,
     author = {Dr\'apal, Ale\v{s}},
     title = {On multiplication groups of left conjugacy closed loops},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {223--236},
     year = {2004},
     volume = {45},
     number = {2},
     mrnumber = {2075271},
     zbl = {1101.20035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2004_45_2_a3/}
}
TY  - JOUR
AU  - Drápal, Aleš
TI  - On multiplication groups of left conjugacy closed loops
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2004
SP  - 223
EP  - 236
VL  - 45
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMUC_2004_45_2_a3/
LA  - en
ID  - CMUC_2004_45_2_a3
ER  - 
%0 Journal Article
%A Drápal, Aleš
%T On multiplication groups of left conjugacy closed loops
%J Commentationes Mathematicae Universitatis Carolinae
%D 2004
%P 223-236
%V 45
%N 2
%U http://geodesic.mathdoc.fr/item/CMUC_2004_45_2_a3/
%G en
%F CMUC_2004_45_2_a3
Drápal, Aleš. On multiplication groups of left conjugacy closed loops. Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 2, pp. 223-236. http://geodesic.mathdoc.fr/item/CMUC_2004_45_2_a3/