An affirmative answer to a question on connectivity of p-subgroup posets with irreducible characters

Gang Chen, Wenhua Zhao

Let $p$ be a prime, $e$ a nonnegative integer, and G a finite p-group with $p^{e+1}$ dividing $|G|$. Let I be the intersection of all subgroups of order $p^{e+1}$ in $G$. It is pro…