Geodesic
On multiplication groups of left conjugacy closed loops
Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 2, pp. 223-236.

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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 
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     author = {Dr\'apal, Ale\v{s}},
     title = {On multiplication groups of left conjugacy closed loops},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {223--236},
     publisher = {mathdoc},
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     zbl = {1101.20035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2004__45_2_a3/}
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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/