Tour:Introduction two (beginners)

Proceed to Guided tour for beginners:Some variations of group

Hopefully, by the time you've reached this part of the guided tour, you have the basic definitions of a group and have some understanding of this definition. In this part, we'll see more about how to prove simple tihngs about groups, and how to manipulate equations in groups.

We'll begin by reviewing some simple examples that we've seen implicitly: equivalence of definitions, and some basic things about manipulating groups. After that, we'll go through some survey articles.

The structure of groups is fairly rigid, because the axioms that control this structure are very strong: associativity, neutral element (identity element), and inverse element. To appreciate this, we'll explore a bit about variations on the structure,and how the powerful axioms of groups make them particularly well-behaved.