Word.ws English Dictionary

How to use automorphism in a sentence

13 example sentences · noun

Automorphism means an isomorphism of a mathematical object or system of objects onto itself. Example: “The automorphism group of a set is the set's symmetric group.”

Examples of automorphism by meaning

nounAn isomorphism of a mathematical object or system of objects onto itself.

  • In mathematics, automorphisms of algebraic structures play an important role.2005, Maninda Agrawal, Nitin Saxena, “Automorpisms of Finite Rings and Applications to Complexity of Problems”, in Volker Diekert, Bruno...
  • A tame automorphism is a product of elementary automorphisms, and a non-tame automorphism is called wild.2014, Alexei Belov, Leonid Bokut, Louis Rowen, Jie-Tai Yu, “The Jacobian Conjecture, Together with Specht and Burnside-Type Problems”, in...

More sentences with automorphism

  • The automorphism group of a set is the set's symmetric group.From the entry automorphism group
  • The study of the automorphisms of splitting fields of separable polynomials over a field is referred to as Galois theory.From the entry separable polynomial
  • The automorphism group of a finite-dimensional vector space (respectively, projective space) is the space's general linear group (respectively, projective linear group).From the entry automorphism group
  • Roughly speaking, chiral polytopes have half as many possible automorphisms as have regular polytopes.2006, Peter McMullen, Egon Schulte, “Regular and Chiral Polytopes in Low Dimensions”, in Harold Scott Macdonald Coxeter, Chandler Davis…. From the entry flag
  • We call P (combinatorially) regular if its automorphism group Γ(P) is transitive on its flags.2002, Peter McMullen, Egon Schulte, Abstract Regular Polytopes, Encyclopedia of Mathematics and Its Applications 92, page 31. From the entry flag
  • One can see this by using the Dynkin diagram instead of the Coxeter diagram and noting that it does not have any nontrivial automorphisms.2008, Peter Abramenko, Kenneth S. Brown, Buildings: Theory and Applications, page 259. From the entry Coxeter diagram
  • An automorphism of a Coxeter diagram M leads in a natural way to a Coxeter subgroup of the Coxeter group of type M.1993, B. Mühlherr, “Coxeter groups in Coxeter groups”, in Albrecht Beutelspacher, F. Buekenhout, J. Doyen, F. de Clerck, J. A. Thas, J. W.…. From the entry Coxeter diagram
  • In this chapter we present the Galois theory which may be described as the analysis of field extensions by means of automorphism groups.1989, G. Karpilovsky, Topics in Field Theory, North-Holland, page 299. From the entry Galois theory
  • In particular, in the case where the boundary holonomy is infinitely tangent to the identity, we determine the structure of the group of leafwise holomorphic automorphisms.2015, Tomohiro Horiuchi, “Reeb components of leafwise complex foliations and their symmetries II”, in arXiv. From the entry leafwise
  • The basic graphs either admit an edge-transitive group of automorphisms that is quasiprimitive or biquasiprimitive on vertices, or admit an (oriented or unoriented) cycle as a normal quotient.2015, Jehan A. Al-bar, Ahmad N. Al-kenani, Najat Mohammad Muthana, Cheryl E. Praeger, Pablo Spiga, “Finite edge-transitive oriented graphs…. From the entry biquasiprimitive
  • Others generalize a formula of P.Hall, replacing the class of abelian p-groups by subclasses, or by isoclinism classes of non-abelian groups, also by replacing automorphism groups by holomorphs, etc.2015, Avinoam Mann, “Some group theoretical mass formulae”, in arXiv. From the entry isoclinism

Meaning of automorphism

  1. noun An isomorphism of a mathematical object or system of objects onto itself.
  2. noun The ascription to others of one's own characteristics or of one's own perceived characteristics.

Full definition of automorphism

Questions about automorphism in a sentence

How do you use automorphism in a sentence?
Automorphism is used as a noun. For example: “The automorphism group of a set is the set's symmetric group.”
What is a short sentence with automorphism?
“In mathematics, automorphisms of algebraic structures play an important role.”
What does automorphism mean?
Automorphism means an isomorphism of a mathematical object or system of objects onto itself.

Source and license

Adapted from Wiktionary: automorphism (page history and authors) and the entries each sentence comes from. Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws chose the sentences, left out offensive ones and quotations older than 1900, and marked the word in each. Wiktionary data of 2026-09-02.

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Cite this page: “How to use automorphism in a sentence.” Word.ws, https://word.ws/sentences/automorphism. Based on Wiktionary, CC BY-SA 4.0.