In general, loops are considered to have very little in the way of algebraic structure and it is for that reason that many authors limit their investigation to loops which
satisfy various other structural conditions. Common examples of such notions are
the left- and right-Bol loop, the Moufang
loop (which is both a left-Bol loop and a right-Bol loop simultaneously), and
the generalized Bol loop.
The above definition of loop is purely algebraic and shouldn't be confused with other notions of loop, such as a closed
curves, a multi-component knot or hitch,
a graph loop, etc.
such that 
and 
for any 
in the quasigroup. All groups
are loops.
