Monogenic loop

This article defines a property that can be evaluated for a loop.
View other properties of loops

ANALOGY: This is an analogue in loop of a property encountered in group. Specifically, it is a loop property analogous to the group property: cyclic group
View other analogues of cyclic group | View other analogues in loops of group properties (OR, View as a tabulated list)

Definition

A monogenic loop is a loop such that there is a single element of the loop that is not contained in any proper subloop.

Note that if a monogenic loop is also a power-associative loop, then it must be a cyclic group.