Subgroups with all finite lifts isomorphic are conjugate

Ido Karshon, Alexander Lubotzky, D. B. McReynolds +2

We show that for non-conjugate subgroups $G_1$ and $G_2$ of a finite group $G$ there exists an extension of $G$ (by a finite group) in which the pre-images of $G_1$ and $G_2$ are n…