1
$\begingroup$

I need a counterexample for this fact that:

If $G$ is supersolvable, so any quotient group of it, is not neccesarily supersolvable. A infinite one is prefered.

Thanks

  • 0
    Dear Ahilum, no problem! I sugges$t$, if you are learning abou$t$ soluble groups in general, $t$o $t$ake a look at Martin Isaacs' "Finite Group Theory". This book is an excellent introduction to the theory of finite groups and discusses supersolvability in some of the exercises, for example. Also, a good book on the theory of *finite* solvable groups is "Finite Soluble groups" by Klaus Doerk and Trevor O. Hawkes.2011-06-01

1 Answers 1

3

This is a nice page about supersolvability:

http://groupprops.subwiki.org/wiki/Supersolvable_group

As stated on that page, this property is preserved by taking quotients.