2015/05/13 by Péter T. Nagy, Nagy, Péter T.
Mathematics · #20N05 #FOS: Mathematics #Group Theory (math.GR) #History and Theory of Mathematics #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.1505.03270
openalex publication_date 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The objectives of this paper is to give a systematic investigation of extension theory of loops. A loop extension is (left, right or middle) nuclear, if the kernel of the extension consists of elements associating (from left, right or middle) with all elements of the loop. It turns out that the natural non-associative generalizations of the Schreier's theory of group extensions can be characterized by different types of nuclear properties. Our loop constructions are illustrated by rich families of examples in important loop classes.