Notes on finite groups

As an escape from having too much to do, I have combined and lightly revised the notes from my MSc course on finite groups, and posted them here.

I tried to steer a middle course between soluble groups and simple groups. The philosophy of the notes is that the main structure theorem for finite groups is the Jordan–Hölder Theorem, which asserts that the building blocks for finite groups are the finite simple groups (and the mortar that holds them together is extension theory). So there are chapters on both simple groups and extension theory. There is also a short chapter on soluble and nilpotent groups.

However, half of the notes consists of a revision of the basics of finite group theory: the definition of a group and basic properties, examples of groups, group actions, Sylow’s Theorem, and composition series.

Students on an MSc course typically have a wide variety of backgrounds; some of them will not have met this basic material, while others will certainly benefit from a reminder.

So the notes are there; if you have a use for them, please go ahead!

About Peter Cameron

I count all the things that need to be counted.
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2 Responses to Notes on finite groups

  1. Pingback: Cameron’s Group Theory Notes « Log24

  2. None says:

    Very good notes. Thanks for sharing. I found a minor typo on page 18, row 5: “Order 4: Let $G$ be an ELEMENT of order 4” -> “… a GROUP of order 4”

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