1
$\begingroup$

The title says it all: Do you know a comprehensive (preferably online) reference about semi-direct products in (finite) group theory?

I would like to know much more about semi-direct products in the context of the classification of finite groups (of small order).

Thank you for your thoughts!

$\endgroup$
  • $\begingroup$ What do you want to know? $\endgroup$ – Qiaochu Yuan Jan 15 '18 at 7:13
  • $\begingroup$ I want to know, for example, given groups $H$ and $N$ and a homomorphism $\psi: H \to \text{Aut}(N)$ how to calculate a presentation for $N \rtimes_\psi H$, or what is the center of $N \rtimes_\psi H$? And more such stuff. $\endgroup$ – Tortoise Jan 15 '18 at 8:10
  • 1
    $\begingroup$ A presentation is given by a presentation of $N$, concatenated with a presentation of $H$, and the additional relations $hnh^{-1} = \varphi(h)(n)$ for all $h, n \in H, N$. I don't think the center has a simple description (see math.stackexchange.com/questions/243327/… for some discussion). Mostly I think you should try to work out what you want to know as exercises. $\endgroup$ – Qiaochu Yuan Jan 15 '18 at 9:56
3
$\begingroup$

There is "algebra, abstract and concrete" by Robert M. Goodman.

It is free and as far as I know only available in PDF form sadly.

The chapter on group products (I assume that is what you mean).

Available here http://homepage.divms.uiowa.edu/~goodman/algebrabook.dir/algebrabook.html

If you require more advanced introduction I recommend Mark Steinberg's text titled "Algebra". The chapters 3 and 5 appear to consider classification if low order as well. Found here https://www.albany.edu/~mark/markbib.html

$\endgroup$
  • $\begingroup$ Thank you! I will check out the references. $\endgroup$ – Tortoise Jan 15 '18 at 10:22

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.