Definition of Abelian group

1. Noun. A group that satisfies the commutative law.

Exact synonyms: Commutative Group
Generic synonyms: Group, Mathematical Group

Definition of Abelian group

1. Noun. (algebra) a group in which the group operation is commutative ¹

¹ Source: wiktionary.com

Abelian Group Pictures

Click the following link to bring up a new window with an automated collection of images related to the term: Abelian Group Images

Lexicographical Neighbors of Abelian Group

 abecedariusesabecedaryabecediariesabecediaryabecedismabecedismsabedabediterolabeggeabegging abeighabeleabelesabeliaabelianabelian group (current term)abelian groupsabelianisationabelianizationabelianized abeliannessabeliasabelisaurabelisauridabelisauridsabelisaursabelmoskabelmosksabelmuskabelmusks

Literary usage of Abelian group

Below you will find example usage of this term as found in modern and/or classical literature:

1. Theory and Applications of Finite Groups by George Abram Miller, Hans Frederick Blichfeldt, Leonard Eugene Dickson (1916)
"Find the number of subgroups with invariants 6, 2 in the abelian group whose ... Every abelian group is generated by its operators of highest order. 5. ..."

2. Encyclopaedia Britannica, a Dictionary of Arts, Sciences, Literature and edited by Hugh Chisholm (1910)
"If S], S.-, Sj S, are the linear substitutions that of an abelian group G and .... An abelian group contains subgroups whose orders arc any given factors of ..."

3. An Introduction to the Modern Theory of Equations by Florian Cajori (1904)
"Every sub-group of an abelian group is itself an abelian group. Ex. 2. If 0i is not Abelian, and GI is a sub-group of 0, then Q is not Abelian. Ex. 3. ..."

4. Proceedings of the American Philosophical Society Held at Philadelphia for by American Philosophical Society (1907)
"As an indirect result of the preceding paragraph we have that the group of isomorphisms of the abelian group of order p" and type (i, i) must always include ..."

5. Science by American Association for the Advancement of Science (1905)
"This fundamental theorem, due to Sylow, is included in the following: Every non-abelian group of order p" contains at least p invariant commutator operators ..."

6. Proceedings of the London Mathematical Society by London Mathematical Society (1905)
"All of these generate a group which is conformal with an abelian group of type (a, 1, 1, ...). As all the invariant cyclic sub-groups of order pa can be ..."