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Glite Dictionary
automorphism

automorphism

1 9.9
A way to rearrange a math object so it looks and behaves the same as before
  • noun
  • /ˌɔːtəˈmɔːrfɪzəm/
  • Specialized
: automorfismo
  • An automorphism is a mapping that transforms a mathematical object into itself while maintaining its structural properties.
  • nontrivial automorphisms

Examples

  • Understanding an automorphism can help mathematicians analyze the symmetries of various algebraic structures.

  • An automorphism is an isomorphism from a set S to itself, a relabeling of the nodes f: S (r) S that preserves the graph's structure.

    Academic text (2011)

  • An automorphism f is nontrivial if it is not the identity function.

    Academic text (2011)

  • Then it goes to isomorphisms and automorphisms really quick.

  • The subgraph H has no nontrivial automorphisms.

    Academic text (2011)

  • In group theory, an automorphism illustrates how a group's structure can remain unchanged under certain transformations.

Surface Forms

automorphism singular
automorphisms plural

Morphology

automorphism = morphism (opaque) = auto + morph + ism

The prefix auto- means 'self', but the term is a specialized mathematical word whose full meaning is not readily inferable for an average B1 learner.

Etymology

The word automorphism comes from auto- ('self') and morph ('form' or 'shape'), the same morph you see in metamorphosis. So an automorphism is like a 'self-form' map that sends something to itself without changing its shape or structure.