AUTOMORPHISM Meaning and
Definition
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An automorphism is a term commonly used in the field of mathematics, especially in the branch of abstract algebra. It refers to a specific type of mathematical structure that preserves the internal properties of the structure itself when subject to certain operations or transformations. More precisely, an automorphism is a bijective function or mapping that satisfies the conditions of being an isomorphism when applied to an object within a particular mathematical structure.
In simpler terms, an automorphism is a transformation within a certain mathematical system that maintains the fundamental structure and relationships of the elements involved. This transformation leaves the structure unchanged, preserving all the characteristics and properties of the original structure. Thus, an automorphism can be seen as a symmetry or self-similarity inherent within the mathematical system.
Automorphisms play a significant role in various mathematical fields, such as group theory, ring theory, and graph theory. They often assist in studying the properties and symmetries of complex structures and forms, providing insight into the nature of the mathematical objects involved. Understanding and analyzing automorphisms can uncover valuable information about the structure and behavior of mathematical systems, facilitating further exploration and advancement in the field of mathematics.
Common Misspellings for AUTOMORPHISM
Etymology of AUTOMORPHISM
The word "automorphism" comes from the combination of two Greek roots: "auto-" meaning "self" and "-morphism" meaning "shape" or "form". So, "automorphism" can be understood as a self-shape or self-form.
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