Equations which preserve the height of variables

Abstract

We define a special class of linear quasigroup functional equations and call them height preserving equations (short for the equations which preserve the height of variables). It is proved that a quasigroup satisfying a height preserving but not Belousov equation is isotopic to an abelian group. The formulas of a general solution are also given. Some results of Belousov are discussed and partially generalized.