# Resource:Example-based coverage articles

This page lists articles that cover a whole range of definitions, proofs and results in group theory, by developing these concepts as examples for some other, related, subject.

For each of these articles, we briefly describe the other subject or context in which the definitions and results are discussed. We also give a list of important definitions, proofs and results that are covered.

## Elementary group theory

This may be of particular interest to beginners, and to people interested in educating beginners through examples.

### Group theory via geometry

This develops many of the basic notions of group theory by looking at various subgroups of the group of transformations of the Euclidean plane, and the relation between them

Ideas touched upon: [Intermediate subgroup condition]], quotient-transitive subgroup property, intersection-closed subgroup property

### Group theory via permutations

This develops many of the basic notions of group theory by looking at various subgroups of the symmetric group over a set (we consider finite as well as infinite sets):

Ideas touched upon: PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]

### Group theory via number theory

This starts off by looking at the particular case of modular arithmetic, and some groups that arise as the additive and multiplicative groups modulo integers. We then proceed to look at certain other groups, which arise in the context of rings of integers. The focus is mainly on Abelian group theory.

Concepts revised: group, Abelian group, cyclic group

Results revised: structure theorem for finitely generated Abelian groups