Conjecture 19.25

by B. Curtin, G. R. Pourgholi

Reference: The Kourovka Notebook

theorem Kourovka.«19.25».kourovka.«19.25» : sorry ↔ ∀ (G H : Type) [inst : Group G] [inst_1 : Group H] [inst_2 : Fintype G] [inst_3 : Fintype H], ∑ g : G, (orderOf g).totient = ∑ h : H, (orderOf h).totient → IsSimpleGroup G → IsSimpleGroup H

Let $G$ and $H$ be finite groups of the same order with $\sum_{g \in G} \phi(|g|) = \sum_{h \in H} \phi(|h|)$, where $\phi$ is the Euler totient function. Suppose that $G$ is simple. Is $H$ necessarily simple?