The Structure of Non-Associative Finite Invertible Loops (NAFIL)*

Abstract

The NAFIL is a finite loop in which every element has a unique (two-sided)inverse. NAFIL loops can be classified into two types: composite (with at least one non-trivial subsystem) and non-composite or plain (without any non-trivial subsystem). This paper deals with the structure of these loops. In particular we shall introduce an important class of composite NAFIL loops called block products.