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Keywords:
LCC loop; multiplication group; inner mapping group; homomorphism
LCC loop; multiplication group; inner mapping group; homomorphism
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.
References:
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