Starting from an involutorial difference loop (P,+) of order n we construct a new loop (L,.) in the same class and possessing 2n elements. The construction was induced by studying a correspondence connecting such loops with complete graphs with parallelism and regular involution sets. We discuss conditions on (P,+) ensuring that the loop (L,.) is a K-loop and we give explicit examples of K-loops obtained with this method. Further generalizations of this technique are proposed as well.
Construction of a class of loops via graphs
ZIZIOLI, Elena
2009-01-01
Abstract
Starting from an involutorial difference loop (P,+) of order n we construct a new loop (L,.) in the same class and possessing 2n elements. The construction was induced by studying a correspondence connecting such loops with complete graphs with parallelism and regular involution sets. We discuss conditions on (P,+) ensuring that the loop (L,.) is a K-loop and we give explicit examples of K-loops obtained with this method. Further generalizations of this technique are proposed as well.File in questo prodotto:
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