Farjoun's question

This article is about a conjecture. View all conjectures and open problems

Statement

Let $H$ be a finite nilpotent homomorphism-closed subgroup of a group $G$. Then, $H$ must be equal to $G$.

A variant of this is the claim that any finite nilpotent nearly closed subgroup of a group must be the whole group.

References

• On a question of Farjoun by Michael Aschbacher, Finite Groups 2003 published by Walter de Gruyter