The quaternion group (q, degree ) is a group of order 8 with two generators a and b subject to the relations a4 = e, b2 = a2, and a degree b degree a = b. to be explicit, the elements of q are e, a, a2, a3, b, a degree b, a degree b, a2 degree b, a3 degree b. for this discussion prompt, research the subject and find an application of the quaternion group that differs from any of your peer's responses. write the cayley table, find the center, and find all cyclic subgroups for q.|