Template:Group-like structures
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Group-like structures. The entries say whether the property is required. | |||||
Totality* | Associativity | Identity | Divisibility | Commutativity | |
---|---|---|---|---|---|
Semicategory | No | Yes | No | No | No |
Category | No | Yes | Yes | No | No |
Groupoid | No | Yes | Yes | Yes | No |
Magma | Yes | No | No | No | No |
Quasigroup | Yes | No | No | Yes | No |
Loop | Yes | No | Yes | Yes | No |
Semigroup | Yes | Yes | No | No | No |
Monoid | Yes | Yes | Yes | No | No |
Group | Yes | Yes | Yes | Yes | No |
Abelian Group | Yes | Yes | Yes | Yes | Yes |
*Closure, which is used in many sources, is an equivalent axiom to totality, though defined differently. |
fr:Modèle:StructuresSemblablesGroupes pl:Szablon:Struktury grupopodobne