Conjugacy closed loops and their multiplication groups

A loop  Q is said to be conjugacy closed if the sets { L x ; x∈ Q} and { R x ; x∈ Q} are closed under conjugation. Let L and R be the left and right multiplication groups of  Q, respectively, and let Inn Q be its inner mapping group. If  Q is conjugacy closed, then there exist epimorphisms L→ InnQ a...

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Bibliographic Details
Published in:Journal of algebra 2004-02, Vol.272 (2), p.838-850
Main Author: Drápal, Aleš
Format: Article
Language:English
Subjects:
Conjugacy closed loop
Multiplication group
Nucleus
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Summary:A loop  Q is said to be conjugacy closed if the sets { L x ; x∈ Q} and { R x ; x∈ Q} are closed under conjugation. Let L and R be the left and right multiplication groups of  Q, respectively, and let Inn Q be its inner mapping group. If  Q is conjugacy closed, then there exist epimorphisms L→ InnQ and R→ InnQ that are determined by L x ↦ R −1 x L x and R x ↦ L −1 x R x . These epimorphisms are used to expose various structural properties of MltQ= LR .
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2003.06.011