If F is inner automorphism , what does this mean ?

Thread starter Maths Lover
Start date Dec 10, 2012
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In summary, an inner automorphism is a type of transformation that preserves the structure of an object by mapping it to itself and maintaining relationships among its elements. It differs from an outer automorphism, which may change the relationships between elements. Being an inner automorphism means preserving internal structure while allowing for changes in external representation. This concept is useful in scientific research as it allows for a deeper understanding of systems and can be applied to real-world systems in various fields of science.

Dec 10, 2012

Maths Lover

hi
if F is inner automorphism , what does this mean ?

I think that if
F : G to G
then
we can write F(x) as
F(x) = g x g^(-1)
for some fixed g in G and all x in G

that means that F moves X to the conjgation x by g

is this right ?

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Dec 10, 2012

algebrat

Yes, I confirmed this on wikipedia.

Dec 16, 2012

Maths Lover

algebrat said:

Yes, I confirmed this on wikipedia.

thank you very much :)

1. What is an inner automorphism?

An inner automorphism is a type of automorphism, which is a transformation that preserves the structure of a mathematical object. In particular, an inner automorphism is a transformation that maps an object to itself, while also preserving the relationships among the elements of the object. It is called "inner" because it is defined in terms of the internal structure of the object, rather than its external representation.

2. How is an inner automorphism different from an outer automorphism?

An outer automorphism is also a type of automorphism, but it differs from an inner automorphism in that it does not preserve the internal structure of the object. Instead, an outer automorphism may change the way the elements of the object are related to each other, without changing the overall structure of the object itself.

3. What does it mean for F to be an inner automorphism?

If F is an inner automorphism, it means that F is a transformation that maps an object to itself while preserving the internal structure of the object. In other words, F does not change the way the elements of the object are related to each other, but may change their external representation.

4. How is an inner automorphism useful in scientific research?

Inner automorphisms are useful in scientific research because they allow us to study the internal structure of objects without being influenced by their external representation. This can help us gain a deeper understanding of the fundamental properties and relationships within a system, which can lead to new discoveries and advancements in various fields of science.

5. Can inner automorphisms be applied to real-world systems?

Yes, inner automorphisms can be applied to a wide range of real-world systems, including physical, chemical, and biological systems. Many scientific models and theories rely on the concept of inner automorphisms to understand and describe the behavior of these systems. For example, the concept of symmetry, which is essential in many areas of science, is closely related to inner automorphisms.