Constructions of Commutative Automorphic Loops |
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| Authors: | Přemysl Jedlička Michael K Kinyon |
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| Institution: | 1. Department of Mathematics, Faculty of Engineering , Czech University of Life Sciences , Prague, Czech Republic;2. Department of Mathematics , University of Denver , Denver, Colorado, USA |
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| Abstract: | A loop whose inner mappings are automorphisms is an automorphic loop (or A-loop). We characterize commutative (A-)loops with middle nucleus of index 2 and solve the isomorphism problem. Using this characterization and certain central extensions based on trilinear forms, we construct several classes of commutative A-loops of order a power of 2. We initiate the classification of commutative A-loops of small orders and also of order p 3, where p is a prime. |
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| Keywords: | Automorphic inner mappings Central extensions Commutative automorphic loop Commutative A-loop Enumeration of A-loops |
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