Difference between revisions of "Template:Group-like structures"

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imported>KamikazeBot
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| style="border-top: 2px solid #303060" colspan=6| '''''Note:'''''  ''A quasigroup with associativity (equivalently, a semigroup with inverses) <br /> already has an [[identity element]], and is therefore a group.''   
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| style="border-top: 2px solid #303060" colspan=6| '''''Note:'''''  ''A quasigroup with associativity (equivalently, a semigroup with <br /> inverses) already has an [[identity element]], and is therefore a group.''   
 
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Revision as of 15:39, 20 September 2012

Requirements of group-like structures
Totality Identity Associativity Inverses Commutativity
Magma Yes No No No No
Unital Yes Yes No No No
Quasigroup Yes No No Yes No
Loop Yes Yes No Yes No
Semigroup Yes No Yes No No
Monoid Yes Yes Yes No No
Group Yes Yes Yes Yes No
Abelian Group Yes Yes Yes Yes Yes
Groupoid No Yes Yes Yes No
Category No Yes Yes No No
Semicategory No No Yes No No
Note: A quasigroup with associativity (equivalently, a semigroup with
inverses) already has an identity element, and is therefore a group.

af:Sjabloon:Groepagtige strukture cs:Šablona:Grupové struktury fr:Modèle:StructuresSemblablesGroupes ja:Template:Group-like structures pl:Szablon:Struktury grupopodobne sv:Mall:Gruppliknande strukturer zh:Template:類群結構