Title Maximal subgroups in quaternion division algebras over Euclidean fields Type Presentation Keywords Maximal subgroups, Primitive groups, Euclidean field Abstract In this paper, we give a proof of the existence of maximal subgroups in the multiplicative group of quaternion algebras over a Euclidean field via the action of orthogonal group on the sphere. Researchers hamidreza dorbidi (First researcher)