Slid Product of Loops: a Generalization

• Published in: Resultate der Mathematik Vol. 65; no. 1-2; pp. 193 - 212
• Main Authors: Pasotti, Stefano, Zizioli, Elena
• Format: Journal Article
• Language: English
• Published: Basel Springer Basel 01-02-2014
• Subjects: Mathematics; Mathematics and Statistics; nuclei; normal subloops; 20N05; regular permutation sets; Loops; slid product
• ISSN: 1422-6383; 1420-9012
• DOI: 10.1007/s00025-013-0340-8

In this paper, following the slid product construction for loops with inverses of Pasotti and Zizioli [J Geom 100(1–2):129–145,
2011
], we present the general setting in order to build up a new loop
(
L
,
⨁
)
starting from loops (
K
, +) equipped with a well ordering “
⪯
”,
(
P
,
+
^
)
and (
P
, +) with the same neutral element. The results established in the aforementioned note are generalized as well. Moreover we investigate the nuclei of
L
, the normality of subloops isomorphic to (
K
, +) and
(
P
,
+
^
)
and discuss some examples.