SYMMETRIES OF QUATERNIONS 2016jaw  V.V. Smolyaninov // IMASH RAS, Moscow, Russia; ITEB RAS, Puschino, Russia
smolian@mail.ru
The modern mathematical definitions of symmetries are reduced to identification of the
appropriate transformation groups. According to such definition, the group algebras
have the symmetries of discrete groups of their basic elements. In a particular, the basic
elements of Hamilton’s quaternion form discrete «quaternionic group» of 8th order.
There are only 5 discrete groups of 8th order, therefore is admitted to speak about
existence 5 of types quaternions, one of which is «hamiltonian quaternion», and others
four are «unhamiltonian quaternions». In job the comparative description all of five types
quaternions is given. With the purpose of unification of comparisons the generalized model
of quaternion is entered.
