I have observed that isomorphism classes are sensitive to abelianness and cyclic property. Why mathematicians thought those as important to classify? Can anyone explain the motivations for choosing abelian property and cyclic property as important one?
2026-03-30 05:01:43.1774846903
How definition of isomorphism is defined?
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Abelianness and cyclicity are considered important properties because they feature in a lot of theorems. Which definitions turn out to be the really important ones in a given mathematical field is not something which is decided.
It is not the case that one or more mathematicians meet up to discuss which properties of groups should be considered important. The process happens naturally and automatically as hundreds or thousands of mathematicians all study the field and publish their results: Suddenly one can look back at the entire theory and conclude that "abelian" and "cyclic" are properties which are used by many mathematicians in many theorems, and therefore they must be important.