abelian group

Summary

abelian group is a mathematical concept^[1]. It has Wikipedia articles in 28 language editions, a strong signal of global cultural recognition.^[2]

Key Facts

• abelian group's instance of is recorded as mathematical concept^[3].
• Niels Henrik Abel is named after abelian group^[4].
• abelian group is a type of nilpotent group^[5].
• abelian group is a type of commutative monoid^[6].
• abelian group is a type of commutative Moufang loop^[7].
• abelian group is a type of Dedekind group^[8].
• abelian group is a type of module^[9].
• abelian group is a type of CA-group^[10].
• abelian group is a type of FC-group^[11].
• abelian group is a type of elementary amenable group^[12].
• abelian group's Commons category is recorded as Abelian groups^[13].
• abelian group is the opposite of non-abelian group^[14].
• abelian group's Stack Exchange tag is recorded as https://mathoverflow.net/tags/abelian-groups^[15].
• abelian group's Stack Exchange tag is recorded as https://math.stackexchange.com/tags/abelian-groups^[16].
• abelian group's has characteristic is recorded as closure^[17].
• abelian group's has characteristic is recorded as associativity^[18].
• abelian group's has characteristic is recorded as identity element^[19].
• abelian group's has characteristic is recorded as inverse element^[20].
• abelian group's has characteristic is recorded as commutative property^[21].
• abelian group's studied by is recorded as group theory^[22].
• abelian group's studied by is recorded as module theory^[23].
• abelian group's on focus list of Wikimedia project is recorded as Wikipedia:Vital articles/Level/4^[24].
• abelian group's maintained by WikiProject is recorded as WikiProject Mathematics^[25].

Body

Definition and Type

abelian group's instance of is recorded as mathematical concept^[3]. Recorded subclass of include nilpotent group^[5], commutative monoid^[6], commutative Moufang loop^[7], Dedekind group^[8], module^[9], and CA-group^[10]. It is the opposite of non-It^[14].

Origins

Niels Henrik Abel is named after abelian group^[4].

Influence

Things named for abelian group include metabelian group^[26]; abelian extension^[27], a mathematical concept^[28]; and abelian category^[29], a mathematical concept^[30].

Why It Matters

abelian group has Wikipedia articles in 28 language editions, a strong signal of global cultural recognition.^[2] It is known by 43 alternative names across languages and contexts.^[31]

Entities named for it include metabelian group^[26]; abelian extension^[27], a mathematical concept^[28]; and abelian category^[29], a mathematical concept^[30].