Groud

A groud or a heap is a Semigroud in which every element is Biunitary. Alternatively, a heap is a Malcev Operation that is Para-associative.

Intuition

A groud is like a sort of "Affine Group"; EG: a group that has forgotten its Identity Element.

Properties

• If $[-,-,-]$ is a Malcev Operation that satisfies the following partial para-associativity condition:

  $[[a,b,c],d,e]=[a,b,[c,d,e]]$

  then $[-,-,-]$ is a groud. This is quite nasty to prove though.