19_25.lean`

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1 declarations, 1 contain sorry, 0 declared as axioms

Conjecture 19.25

by B. Curtin, G. R. Pourgholi

Reference: The Kourovka Notebook

Imports (1)

FormalConjecturesUtil

theorem Kourovka.«19.25».kourovka_19_25 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 sorry line 41 source
Source documentation
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?

depends on sorry what this means
Statement uses: Iff, True, Group, Fintype, Eq, Nat, Fintype.card, Finset.sum, Finset.univ, Nat.totient, orderOf, IsSimpleGroup
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat
7 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem kourovka_19_25 : answer(sorry) ↔
    ∀ (G H : Type) [Group G] [Group H] [Fintype G] [Fintype H],
       Fintype.card G = Fintype.card H →
       ∑ g : G, φ (orderOf g) = ∑ h : H, φ (orderOf h) →
       IsSimpleGroup G → IsSimpleGroup H := by
…
```