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On this page you'll find 10+ example sentences with Automorphisms. Discover the meaning, how to use the word correctly in a sentence.

Rare word

Automorphisms in a sentence

Related words

Automorphisms | Automorphism

Automorphisms meaning

plural of automorphism

Using Automorphisms

  • The main meaning on this page is: plural of automorphism
  • In the example corpus, automorphisms often appears in combinations such as: automorphisms of, inner automorphisms, field automorphisms.

Context around Automorphisms

  • Average sentence length in these examples: 22.3 words
  • Position in the sentence: 2 start, 6 middle, 7 end
  • Sentence types: 15 statements, 0 questions, 0 exclamations

Often before:

inner 3× field 3× outer 2× identity 1× nontrivial 1× transformations 1×

Sentence patterns with Automorphisms

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

all inner automorphisms is called 1× also outer automorphisms 1× called nontrivial automorphisms 1× equivalent under automorphisms 1× group of automorphisms as a 1× group of automorphisms of this 1× non identity automorphisms are called 1× nontrivial field automorphisms 1×

Sentence openings and endings

Common sentence openings:

for every group 1× however unlike the 1× in the case 1× in the cases 1× non abelian groups 1× normal subgroup main 1×

Common sentence endings:

also outer automorphisms 1× an invariant subgroup 1× as a subgroup 1× by aut g 1× called nontrivial automorphisms 1× domain onto itself 1×

Words around Automorphisms

Just before it in the word index:

automorphism 31 automorphic 9 automobility 2 automobili 3 automobiles 342 automobile 663

Just after it in the word index:

automotion 2 automotive 1.091 automotives 2 auton 2 autonation 35 autonav 5

Similar in corpus frequency:

aaon 19 abbv 19 abdalla 19 abdirahman 19 abdulmalik 19 abhimanyu 19

Corpus analysis for Automorphisms

  • In this selection, "automorphisms" usually appears near the end of the sentence. The average example has 22.3 words, and this corpus slice is mostly made up of statements.
  • Around the word, inner, field and outer stand out and add context to how "automorphisms" is used.
  • Recognizable usage signals include all inner automorphisms is called and also outer automorphisms. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "automorphisms" sits close to words such as aaon, abbv and abdalla, which helps place it inside the broader word index.

Example types with automorphisms

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

Respectively, other (non-identity) automorphisms are called nontrivial automorphisms. (9 words)

These 7 maximal orders are all equivalent under automorphisms. (9 words)

Non-abelian groups have a non-trivial inner automorphism group, and possibly also outer automorphisms. (15 words)

Longer example sentences

For every group G there is a natural group homomorphism G → Aut(G) whose image is the group Inn(G) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group. (46 words)

Some subfields of R have nontrivial field automorphisms, which however do not extend to all of R (because they cannot preserve the property of a number having a square root in R). (32 words)

The set of all automorphisms of a group G, with functional composition as operation, forms itself a group, the automorphism group of G. It is denoted by Aut(G). (29 words)

Example sentences (15)

Respectively, other (non-identity) automorphisms are called nontrivial automorphisms.

For every group G there is a natural group homomorphism G → Aut(G) whose image is the group Inn(G) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.

However unlike the case of finite fields, the Frobenius automorphism on has infinite order, and it does not generate the full group of automorphisms of this field.

In the case of groups, the inner automorphisms are the conjugations by the elements of the group itself.

In the cases of the rational numbers (Q) and the real numbers (R) there are no nontrivial field automorphisms.

Non-abelian groups have a non-trivial inner automorphism group, and possibly also outer automorphisms.

Normal subgroup main A subgroup of H that is invariant under all inner automorphisms is called normal ; also, an invariant subgroup.

Some subfields of R have nontrivial field automorphisms, which however do not extend to all of R (because they cannot preserve the property of a number having a square root in R).

Advertentie

Specifically, the Galois group of F over E, denoted Gal(F/E), is the group of field automorphisms of F that are trivial on E (i.

Tarski's proposal was to demarcate the logical notions by considering all possible one-to-one transformations ( automorphisms ) of a domain onto itself.

That is, there are automorphisms of which are not a power of the Frobenius map.

The isotopy group of an algebra is the group of all isotopies, which contains the group of automorphisms as a subgroup.

The quotient group Aut(G) / Inn(G) is usually denoted by Out(G); the non-trivial elements are the cosets that contain the outer automorphisms.

These 7 maximal orders are all equivalent under automorphisms.

The set of all automorphisms of a group G, with functional composition as operation, forms itself a group, the automorphism group of G. It is denoted by Aut(G).

Advertentie

Common combinations with automorphisms

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "automorphisms" in a sentence?
An example: "Respectively, other (non-identity) automorphisms are called nontrivial automorphisms." This page contains 10+ example sentences with the word "automorphisms" from authentic English texts.
What does "automorphisms" mean?
Automorphisms means: plural of automorphism
How many example sentences with "automorphisms" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "automorphisms", drawn from a database of millions of English sentences.