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 8-th order. There are only 5 discrete groups of 8-th 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.