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Recall that a subgroup $H$ of a group $G$ is called a TI-subgroup if for every $g \in G$ one has $H \cap H^g \in \{1,H\}$. We say that a group $G$ is a DTI-group if the derived subgroups of all of its subgroups are TI-subgroups of $G$.

Question: Is the class of DTI-groups closed under taking quotients?

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  • $\begingroup$ An immediate observation is that the class of DTI-groups is closed under taking subgroups. $\endgroup$
    – Stefan Kohl ♦
    Commented Apr 5, 2022 at 19:10
  • $\begingroup$ If $H$ is a subgroup of $G$, and $K$ is a subgroup of $H$, is your definition wanting $K'$ to be TI in $G$ or $H$? $\endgroup$
    – zibadawa timmy
    Commented Apr 6, 2022 at 1:05
  • $\begingroup$ @zibadawa timmy $K'$ is TI in $G$. I.e. the derived subgroup of every subgroup of $G$ is a TI-subgroup of $G$. $\endgroup$
    – Leyli Jafari
    Commented Apr 6, 2022 at 1:28

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