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1MileCrash
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If p is an automorphism on G, and H and K are subgroups of G, does p(H intersect K) = p(H) intersect p(K)?
If so, how can I show this?
EDIT: nevermind
If so, how can I show this?
EDIT: nevermind
Last edited:
Automorphisms are mathematical transformations that preserve the structure and properties of a mathematical object. They are essentially "symmetries" of the object.
Automorphisms are important in mathematics as they help in understanding the underlying structure and properties of a mathematical object. They also have a wide range of applications in various fields, such as group theory, graph theory, and algebraic geometry.
The process of finding automorphisms depends on the specific mathematical object in question. In general, it involves analyzing the structure and properties of the object and determining which transformations preserve those properties.
No, not all mathematical objects have automorphisms. For example, a line segment does not have any non-trivial automorphisms, while a square has four. The existence of automorphisms depends on the structure and properties of the object.
An automorphism is a transformation that preserves the structure and properties of a mathematical object, while an isomorphism is a type of automorphism that is also bijective (one-to-one and onto). In other words, all isomorphisms are automorphisms, but not all automorphisms are isomorphisms.