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!

  • $\begingroup$ What do you want to know? $\endgroup$ Jan 15, 2018 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, 2018 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. $\endgroup$ Jan 15, 2018 at 9:56

1 Answer 1


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


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