## Definitions for abelian group

### Princeton's WordNet(0.00 / 0 votes)Rate this definition:

1. Abelian group, commutative group(noun)

a group that satisfies the commutative law

### Wiktionary(0.00 / 0 votes)Rate this definition:

1. abelian group(Noun)

a group in which the group operation is commutative

### Freebase(0.00 / 0 votes)Rate this definition:

1. Abelian group

In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on their order. Abelian groups generalize the arithmetic of addition of integers. They are named after Niels Henrik Abel. The concept of an abelian group is one of the first concepts encountered in undergraduate abstract algebra, with many other basic objects, such as a module and a vector space, being its refinements. The theory of abelian groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood. On the other hand, the theory of infinite abelian groups is an area of current research.

### Numerology

1. Chaldean Numerology

The numerical value of abelian group in Chaldean Numerology is: 8

2. Pythagorean Numerology

The numerical value of abelian group in Pythagorean Numerology is: 4

# Translations for abelian group

### From our Multilingual Translation Dictionary

• abelovská grupa
• kommutative Gruppe, abelsche Gruppe
• grupo abeliano
• groupe abélien
• Abel-csoport
• Abel-grúpa, víxlin grúpa, abelsk grúpa, víxlgrúpa
• gruppo abeliano
• アーベル群
• grupa abelowa, grupa przemienna
• grupo abeliano
• grup abelian
• а́белева гру́ппа
• Abelova grupa
• kommutativ grupp, abelsk grupp
• ఎబిలియన్ సమూహం

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"abelian group." Definitions.net. STANDS4 LLC, 2017. Web. 17 Dec. 2017. <http://www.definitions.net/definition/abelian group>.