Introduction: Non-Associative Finite Invertible Loops

Details Introduction: Non-Associative Finite Invertible Loops Introduction: Non-Associative Finite Invertible Loops

2009-07-29

arxiv.org/abs/0907.5059v1

Mathematics

Group Theory

Scientific paper

Non-associative finite invertible loops (NAFIL) are loops whose every element has a unique two-sided inverse. Not much is known about the class of NAFIL loops which includes the familiar IP (Inverse Property), Moufang, and Bol loops. Our studies have shown that they are involved in such diverse fields as combinatorics, finite geometries, quasigroups and related systems, Cayley algebras, as well as in theoretical physics. This paper presents and introductions to the class of NAFIL loops as the starting point for the development of the theory of these interesting structures.

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