group

Summary

group is a mathematical concept^[1]. group ranks in the top 2% of mathematical_concept entities by monthly Wikipedia readership (8,246 views/month).^[2]

Key Facts

• group's instance of is recorded as mathematical concept^[3].
• group is a type of monoid^[4].
• group is a type of inverse semigroup^[5].
• group is a type of Moufang loop^[6].
• group is a type of groupoid^[7].
• group is a type of epigroup^[8].
• group is a type of algebraic structure^[9].
• group is a type of group object^[10].
• group is a type of loop^[11].
• group's Commons category is recorded as Group theory^[12].
• group comprises set^[13].
• group comprises binary operation^[14].
• group comprises identity element^[15].
• group comprises inverse^[16].
• group's topic's main category is recorded as Q13324638^[17].
• group's described by source is recorded as Q140169500^[18].
• group's topic has template is recorded as Template:Group navbox^[19].
• group's has characteristic is recorded as closure^[20].
• group's has characteristic is recorded as associativity^[21].
• group's has characteristic is recorded as identity element^[22].
• group's has characteristic is recorded as inverse element^[23].
• group's has characteristic is recorded as Latin square property^[24].
• group's different from is recorded as group^[25].
• group's properties for this type is recorded as P1164^[26].
• group's has list is recorded as Examples of groups^[27].

Body

Definition and Type

group's instance of is recorded as mathematical concept^[3]. Recorded subclass of include monoid^[4], inverse semigroup^[5], Moufang loop^[6], groupoid^[7], epigroup^[8], and algebraic structure^[9].

Use and Application

Components include set^[13], a primitive notion^[28]; binary operation^[14]; identity element^[15]; and inverse^[16], a mathematical concept^[29].

Why It Matters

group ranks in the top 2% of mathematical_concept entities by monthly Wikipedia readership (8,246 views/month).^[2] group has Wikipedia articles in 30 language editions, a strong signal of global cultural recognition.^[30] group is known by 39 alternative names across languages and contexts.^[31]