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Get to know Abelianization better with 3 real example sentences, the meaning.

Rare word

Abelianization in a sentence

Abelianization meaning

A homomorphism that transforms a group into an abelian group.

Using Abelianization

  • The main meaning on this page is: A homomorphism that transforms a group into an abelian group.
  • In the example corpus, abelianization often appears in combinations such as: the abelianization.

Context around Abelianization

  • Average sentence length in these examples: 23.7 words
  • Position in the sentence: 1 start, 0 middle, 2 end
  • Sentence types: 3 statements, 0 questions, 0 exclamations

Often after:

functor 1×

Sentence patterns with Abelianization

These short patterns come directly from the example sentences and show how the word is often embedded:

group s abelianization 1× the abelianization functor is 1× to the abelianization of π 1×

Sentence openings and endings

Common sentence openings:

see above for 1× the abelianization functor 1×

Common sentence endings:

category of groups 1× group s abelianization 1×

Words around Abelianization

Just before it in the word index:

abelian 112 abeles 3 abeler 2 abele 6 abelardo 4 abelard 13

Just after it in the word index:

abelido 4 abell 24 abella 10 abellana 3 abelleira 2 abellio 4

Similar in corpus frequency:

aaaaand 5 aaah 5 aacl 5 aak 5 aapke 5 aarav 5

Corpus analysis for Abelianization

  • In this selection, "abelianization" usually appears near the end of the sentence. The average example has 23.7 words, and this corpus slice is mostly made up of statements.
  • Around the word, functor stand out and add context to how "abelianization" is used.
  • Recognizable usage signals include group s abelianization and the abelianization functor is. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "abelianization" sits close to words such as aaaaand, aaah and aacl, which helps place it inside the broader word index.

Example types with abelianization

The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:

Short example sentences

See above for the definition of a group's abelianization. (10 words)

The abelianization functor is the left adjoint of the inclusion functor from the category of abelian groups to the category of groups. (22 words)

If X is path-connected, then this homomorphism is surjective and its kernel is the commutator subgroup of π 1 (X, x 0 ), and H 1 (X) is therefore isomorphic to the abelianization of π 1 (X, x 0 ). (39 words)

Longer example sentences

If X is path-connected, then this homomorphism is surjective and its kernel is the commutator subgroup of π 1 (X, x 0 ), and H 1 (X) is therefore isomorphic to the abelianization of π 1 (X, x 0 ). (39 words)

The abelianization functor is the left adjoint of the inclusion functor from the category of abelian groups to the category of groups. (22 words)

See above for the definition of a group's abelianization. (10 words)

Example sentences (3)

If X is path-connected, then this homomorphism is surjective and its kernel is the commutator subgroup of π 1 (X, x 0 ), and H 1 (X) is therefore isomorphic to the abelianization of π 1 (X, x 0 ).

See above for the definition of a group's abelianization.

The abelianization functor is the left adjoint of the inclusion functor from the category of abelian groups to the category of groups.

Common combinations with abelianization

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "abelianization" in a sentence?
An example: "If X is path-connected, then this homomorphism is surjective and its kernel is the commutator subgroup of π 1 (X, x 0 ), and H 1 (X) is therefore isomorphic to the abelianization of π 1 (X, x 0 )." This page contains 3 example sentences with the word "abelianization" from authentic English texts.
What does "abelianization" mean?
Abelianization means: A homomorphism that transforms a group into an abelian group.
How many example sentences with "abelianization" are there?
Voorbeeldzinnen.info contains 3 example sentences with "abelianization", drawn from a database of millions of English sentences.