Right Feeble Groups

Abstract

Right feeble groups are defined as groupoids $(X,\ast )$ such that (i) $x,y\in X$ implies the existence of $a,b\in X$ such that $a\ast x=y$ and $b\ast y=x$. Furthermore, (ii) if $x,y,z\in X$ then there is an element $w\in X$ such that $x\ast (y\ast z)=w\ast z$. These groupoids have a "remnant" group structure, which includes many other groupoids. In this paper, we investigate some properties of these groupoids. Enough examples are supplied to support the argument that they form a suitable class for systematic investigation.

submitted