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We study the existence and cardinality of normal geodesics of differentcausal types on H(eisenberg)-type quaternion group equipped with thesub-Lorentzian metric. We present explicit formulas for geodesics and describereachable sets by geodesics of different causal character. We compare resultswith the sub-Riemannian quaternion group and with the sub-Lorentzian Heisenberggroup, showing that there are similarities and distinctions. We show that thegeodesics on H-type quaternion groups with the sub-Lorentzian metric satisfythe equations describing the motion of a relativistic particle in a constanthomogeneous electromagnetic field.

Geodesics on H-type quaternion groups with sub-Lorentzian metric and their physical interpretation