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Leyli Jafari
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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?

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.

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

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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YCor
YCor
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Recall that a subgroup $H$ of a group $G$ is called a TI-subgroup if for every $g \in G$ it isone 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.

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

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

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

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.

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

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Leyli Jafari
Leyli Jafari
  • 347
  • 4
  • 13

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

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

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