1
$\begingroup$

When does all normal subgroups of a group have complement? This question is different from question When does a subgroup H of a group G have a complement in G?

Related to this question I ask is following https://math.stackexchange.com/questions/1824173/complement-of-normal-subgroups-and-free-groups

Improve this question
$\endgroup$
4
  • $\begingroup$ When $G$ is simple for example. I think the question is too broad. $\endgroup$
    – Derek Holt
    Commented Jun 13, 2016 at 10:09
  • $\begingroup$ If $G$ is a semi-direct product of $H$ and $G/H$. en.wikipedia.org/wiki/… $\endgroup$
    – Ian Agol
    Commented Jun 13, 2016 at 11:31
  • $\begingroup$ although I had asked for some kind of classification or well known theorems like en.wikipedia.org/wiki/Schur-Zassenhaus_theorem. But I just want clarification on your comment. If G isomorphic to semidirect product of H and G/H, Isomorphic image of {e}*G/H will be required subspace, right? $\endgroup$
    – Sushil
    Commented Jun 13, 2016 at 11:44
  • $\begingroup$ By the way, the question in the title is different from the question in the first sentence of the body; Ian Agol is answering the question in the title. $\endgroup$
    – Derek Holt
    Commented Jun 13, 2016 at 12:07

0

Reset to default

Browse other questions tagged .