19.74 (2018)

A subgroup $H$ of a group $G$ is called pronormal if $H$ and $H^g$ are conjugate in $\langle H, H^g \rangle$ for every $g \in G$. A subgroup $H$ of a group $G$ is called abnormal if $g \in \langle H, H^g \rangle$ for every $g \in G$. Does there exist an infinite group that does not contain nontrivial proper pronormal subgroups?

The question is equivalent to the following: does there exist an infinite simple group that does not contain proper abnormal subgroups?