The quaternion group, usually written Q8, is a non-abelian group of order eight built from the eight-element subset {1, i, j, k, -1, -i, -j, -k} of the quaternions under multiplication. It can be presented by generators and relations discovered by William Rowan Hamilton, whose same relations also generate the quaternions themselves as an algebra over the real numbers. Like many other finite groups, the quaternion group can be realized as the Galois group of a certain field of algebraic numbers.
Facts
Partially Attested
Origin YearThis is the year Hamilton discovered the i, j, k relations; the article does not give a separate year for when the eight-element group itself was first treated as a group. Classification
Object KindStructure or Algebraic Object 1 Connections
Is Kind Of Object
Entity-backed identity for the object-kind enum value this mathematical object already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The object-kind fact itself stays on the object unchanged.
Sources
1. Wikipedia: Quaternion group
Introduction sectionQuote, Introduction section
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.
2. Wikipedia: Quaternion
History sectionQuote, History section
The great breakthrough in quaternions finally came on Monday 16 October 1843 in Dublin, when Hamilton was on his way to the Royal Irish Academy to preside at a council meeting.
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