  The class of non-commutative hypercomplex number systems (HNS) of
4-dimension, constructed by using of non-commutative Grassmann-Clifford
procedure of doubling of 2-dimensional systems is investigated in the article
and established here are their relationships with the generalized quaternions.
Algorithms of performance of operations and methods of algebraic
characteristics calculation in them, such as conjugation, normalization, a type
of zero divisors are investigated. The considered arithmetic and algebraic
operations and procedures in this class HNS allow to use these HNS in
mathematical modeling.
