Quaternion group
Non-abelian group of order eight / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Quaternion group?
Summarize this article for a 10 year old
SHOW ALL QUESTIONS
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
More information i, j ...
1 | i | j | k | |
---|---|---|---|---|
1 | 1 | i | j | k |
i | i | −1 | k | −j |
j | j | −k | −1 | i |
k | k | j | −i | −1 |
Close
where e is the identity element and e commutes with the other elements of the group. These relations, discovered by W. R. Hamilton, also generate the quaternions as an algebra over the real numbers.
Another presentation of Q8 is
Like many other finite groups, it can be realized as the Galois group of a certain field of algebraic numbers.[1]