What Is Quaternion Group?

In group theory, the quaternion group Q₈ is a non-abelian group of order eight, isomorphic to the eight-element subset \{1, i, j, k, -1, -i, -j, -k\} of the quaternions under multiplication.

What is quaternion group in group theory?

In group theory, the quaternion group Q₈ (sometimes just denoted by Q) is a non-abelian group of order eight, isomorphic to the eight-element subset of the quaternions under multiplication. It is given by the group presentation. where e is the identity element and e commutes with the other elements of the group.

Is the quaternion group abelian?

The quaternion group is a non-abelian group of order eight.