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Questions about the branch of algebra that deals with groups.

17 votes

Why do Groups and Abelian Groups feel so different?

It almost seems that the "non" in non-abelian is a positive quality. I remember my advisor saying that "nonlinear" isn't a hypothesis but the absence of a hypothesis. In that sense "nonlinear" mea …
John D. Cook's user avatar
  • 5,217
36 votes
17 answers
6k views

Canonical examples of algebraic structures

Please list some examples of common examples of algebraic structures. I was thinking answers of the following form. "When I read about a [insert structure here], I immediately think of [example]." O …