group
algebraic set with an invertible, associative internal operation admitting a neutral element
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Summary
group is a mathematical concept[1]. group ranks in the top 2% of mathematical concept entities by monthly Wikipedia readership (6,354 views/month).[2]
Key Facts
- Subclass of: monoid[3], inverse semigroup[4], Moufang loop[5], groupoid[6], epigroup[7], algebraic structure[8], group object[9], loop[10]
- Commons category: Group theory[11]
- Has part(s): set[12], binary operation[13], identity element[14], inverse[15]
- Topic's main category: Q13324638[16]
- Described by source: Mathwords[17]
- Topic has template: Template:Group navbox[18]
- Has characteristic: closure[19], associativity[20], identity element[21], inverse element[22], Latin square property[23]
- Different from: group[24]
- Properties for this type: P1164[25]
- Has list: Examples of groups[26]
- Studied by: group theory[27], category theory[28], abstract algebra[29]
- Exact match: http://www.farzanegi.org/math/Group?lang=PA[30]
- On focus list of Wikimedia project: Wikipedia:Vital articles/Level/4[31]
- Maintained by WikiProject: WikiProject Mathematics[32]
- P14534: Group[33]
Why It Matters
group has Wikipedia articles in 30 language editions, a strong signal of global cultural recognition.[34] group is known by 39 alternative names across languages and contexts.[35]