Examples of automorphism

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Here we study some of their basic properties, such as their automorphism group, diameter, and spectrum.
In the final section, we show that any symmetry of the dynamical system gives rise to an automorphism of the algebra.
R is called hyperfinite if it can be generated by a single automorphism.
At the same time we see that the automorphism constructed there is isotopic to the identity automorphism of the algebra.
Finally, it is easy to see that the automorphism group of a stable map (over a field) is finite (the weights only help).
In fact an inner automorphism that preserves such a triple is trivial while any two such triples are conjugate.
The twisted odd graphs are obtained from the well-known odd graphs through an involutive automorphism.
To prove that it is an automorphism, we exhibit an inverse.
These basic properties are used to compute the dual entropy of an arbitrary automorphism of a crystallographic group.
Then, we can see that 2 = and, hence, is an automorphism.
Note that the parameter does not appear in the formulas; its only role is to specify the algebra on which the automorphism acts.
We show that symmetry, represented by a graph's automorphism group, can be used to greatly reduce the computational work for the substitution method.
However, the notion of automorphism associated with groups is in some sense too 'trivial' for characterising the symmetry involved in a reversible computation.
Similarly, the kernel of the action of the outer automorphism group of a free group is finitely generated and residually torsion-free nilpotent.
The conjugacy is an automorphism of the torus and, thus, is not homotopic to identity.
We must now show that every matroid automorphism is obtained in this manner.

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