Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. Plural form of automorphism.
Etymologies
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Examples

The basis elements of the automorphisms are e_a = ?
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In his hands, it turned from the study of substitutions in formulas and of functions invariant under such substitutions into the study of field extensions and corresponding automorphisms (Stein 1988, earlier Mehrtens 1979b).

“NFU can be understood as the theory of certain nonstandard models of Zermelostyle set theory with automorphisms”

It is again a relative concept and, again, a group of automorphisms of the space is involved.

From this approach, an “obvious” asymmetry is frequently a regular symmetry with respect to a group of automorphisms that are not strict orthogonal trans  formations but obvious distortions of such.

By this is meant that any point P of the space can be carried into any other point Q by at least one of the automorphisms.

In order to arrive at a general mathe  matically oriented notion of symmetry, it is also neces  sary to consider not only single automorphisms but certain assemblages of automorphisms called groups

The symmetry of a figure is “interesting,” or “mean  ingful,” or “relevant,” mathematically or aesthetically, if the automorphisms of the underlying group are

Now, the mathematical notion of symmetry demands that there shall be given some group of automorphisms.

A figure is not just symmetric tout court, but it is symmetric relative to a given group of automorphisms, which, in a logical sense, has to be given first.
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