Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

Quasigroup

In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure that resembles a group in the sense that "division" is always possible. Quasigroups differ from groups mainly in that the associative and identity element properties are optional. In fact, a nonempty associative quasigroup is a group.

Definitions, Examples & Loops

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Research this topic

Explore the main themes, entities and connections around Quasigroup. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

Definitions

Loops

Symmetries

Examples

Properties

Morphisms

Generalizations

Number of small quasigroups and loops

  • OEIS On-Line Encyclopedia of Integer Sequences

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

Map overview Semantic statistics

Quasigroup

Nodes77
Edges76
Triples85
Avg. degree1.97
Density0.025974
Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

Quasigroup

Top relations

related to Examples · 15
Quasigroup → An, Any, Every, Every Steiner, F4, Galois, Hans Zassenhaus, More, Moufang, On, See, Steiner, The, These, Z/3Z
related to Total symmetry · 8
Quasigroup → Another, GECC, Generalized Elliptic Cubic Curve, Idempotent, Steiner, The, TS-quasigroup, Without
related to Algebra · 7
Quasigroup → Cayley, Each, In, Latin, The, This, With
is a · 6
Quasigroup → algebraic structure that resembles a group in the sense that, bijection of Q to itself, group.A quasigroup that has an identity element is called a loop..mw-parser-output .hlist dl, Latin square, ordinary quasigroup.An example of a multiary quasigroup is an iterated group operation, set with an n-ary operation
related to External links · 6
Quasigroup → Archived, EMS Press, Encyclopedia, Mathematics, Quasi-group, Wayback Machine
related to Conjugation (parastrophe) · 4
Quasigroup → Any, From, Left, That
related to Inverse properties · 4
Quasigroup → Every, Lx, Rx, The
related to Latin squares · 4
Quasigroup → Conversely, Latin, See Small Latin, The
related to Number of small quasigroups and loops · 4
Quasigroup → A057771, A057991, OEIS, The
related to Properties · 4
Quasigroup → Quasigroups, Similarly, The Latin, This

Important terminology Word statistics

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

group loop quasigroups left element operations division identity operation right inverse set property multiplication every called latin algebra given binary

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Quasigroupis aalgebraic structure that resembles a group in the sense that0.90text
Quasigroupis agroup.A quasigroup that has an identity element is called a loop..mw-parser-output .hlist dl0.90text
Quasigroupis aLatin square0.90text
Quasigroupis aset with an n-ary operation0.90text
Quasigroupis abijection of Q to itself0.90text
Quasigroupis aordinary quasigroup.An example of a multiary quasigroup is an iterated group operation0.90text
Quasigrouprelated to AlgebraLatin0.60section
Quasigrouprelated to AlgebraThis0.60section
Quasigrouprelated to AlgebraIn0.60section
Quasigrouprelated to AlgebraEach0.60section
Quasigrouprelated to AlgebraCayley0.60section
Quasigrouprelated to AlgebraThe0.60section

Related concept clusters Concept neighborhoods

These clusters group vocabulary that occurs around closely connected concepts in the source material.

    Connections between topic areas Semantic bridges

    Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

    Min side: 3
    For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.