Piroska Cs\"org\H o
Extending the structural homomorphism of LCC loops

Comment.Math.Univ.Carolinae 46,3 (2005) 385-389.

Abstract: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 Dr\'apal'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.

Keywords: LCC loop, multiplication group, inner mapping group, homomorphism
AMS Subject Classification: 20D10, 20N05