On left conjugacy closed loops with a nucleus of index two

  • A. Dräpal


A loop Q is said to be left conjugacy closed (LCC) if the left translations form a set of permutations that is closed under conjugation. Loops in which the left and middle nuclei coincide and are of index 2 are necesarilly LCC, and they are constructed in the paper explicitly. LCC loops Q with the right nucleus G of index 2 offer a larger diversity, but that is associated with the level of commutativity of G (amongst others, the centre of G has to be nontrivial). On the other hand, for each m ≥ 2 one can construct an LCC loop Q of order 2m in such a way that its left nucleus is trivial, and the right nucleus if of order m. If Q is involutorial, then it is a Bol loop.

2000 Mathematics Subject Classification

Primary 20N05 Secondary 08A05 

Key words and phrases

Left conjugacy closed loop nucleus 


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Copyright information

© Mathematische Seminar 2004

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsCharles UniversityPraha 8Czech Rep.

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