Quaternion group
id:
quaternion-group-221-2519664
title:
Quaternion group
text:
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 { 1, i, j, k, − 1, − i, − j, − k } of the quaternions under multiplication. It is given by the group presentation
- Q 8 = ⟨ e ¯, i, j, k ∣ e ¯ 2 = e, i 2 = j 2 = k 2 = i j k = e ¯ ⟩, 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 a
brand slug:
wiki
category slug:
encyclopedia
description:
Non-abelian group of order eight
original url:
https://en.wikipedia.org/wiki/Quaternion_group
date created:
2002-11-30T02:28:49Z
date modified:
2024-09-13T19:00:10Z
main entity:
{"identifier":"Q1335680","url":"https://www.wikidata.org/entity/Q1335680"}
image:
{"content_url":"https://upload.wikimedia.org/wikipedia/commons/5/5f/Cyclic_group.svg","width":443,"height":431}
fields total:
13
integrity:
16