====== Josh's outline ======

===== Introduction =====
The goal is to produce a set of IBL notes that works from the definition of a [[Definition:Group|group]] to [[Theorem:Sylow's Theorem]]. The primary point of view will be that of [[Definition:Permutation Group|permutation groups]] with the abstract definition of a [[Definition:Group|group]] being preceded by exploring concrete examples of [[Definition:Automorphism Group|automorphism groups]].

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===== Prerequisites =====
  * Linear algebra


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===== The outline =====

==== First definitions and examples ====

{{page>problem:Simple Matrix Encryption#problem&link&noeditbutton&nofooter&inline}}

{{page>definition:Symmetric group#definition&link&noeditbutton&nofooter&inline}}

{{page>problem:Diagramatic representation of Sn#problem&link&noeditbutton&nofooter&inline}} 

{{page>definition:Automorphism of a graph#definition&link&noeditbutton&nofooter&inline}}

{{page>problem:Aut-square#problem&link&noeditbutton&nofooter&inline}}

{{page>definition:Group#definition&link&noeditbutton&nofooter&inline}}

{{page>problem:Explicit examples of abstract groups#problem&link&noeditbutton&nofooter&inline}}

{{page>definition:Order (for groups)#definition&link&noeditbutton&nofooter&inline}}

{{page>definition:Abelian group#definition&link&noeditbutton&nofooter&inline}}

{{page>definition:Subgroup#definition&link&noeditbutton&nofooter&inline}}

{{page>problem:Examples of abstract groups#problem&link&noeditbutton&nofooter&inline}}

{{page>theorem:Intersection of subgroups is a subgroup#theorem&link&noeditbutton&nofooter&inline}}