20_76.lean`

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

1 declarations, 1 contain sorry, 0 declared as axioms

Conjecture 20.76

by L. Pyber Reference: The Kourovka Notebook !

Imports (1)

FormalConjecturesUtil

theorem Kourovka.«20.76».kourovka_20_76 Let $G$ be a finite $p$-group and assume that all abelian normal subgroups of $G$ have order at most $p^k$ sorry line 34 source
Source documentation
Let $G$ be a finite $p$-group and assume that all abelian normal subgroups of $G$ have order at most $p^k$. Is it true that every abelian subgroup of $G$ has order at most $p^{2k}$?

depends on sorry what this means
Statement uses: Iff, True, Nat, Nat.Prime, Group, IsPGroup, Finite, Subgroup, And, Subgroup.Normal, IsMulCommutative, Subtype, Membership.mem, LE.le, Nat.card, HPow.hPow, HMul.hMul, OfNat.ofNat
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
22 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem kourovka_20_76 : answer(sorry) ↔
    ∀ᵉ (p : ℕ) (hp : p.Prime) (G : Type) (_ : Group G) (hg : IsPGroup p G) (_ : Finite G) (k : ℕ)
    (h : ∀ H: Subgroup G, H.Normal ∧ IsMulCommutative H → Nat.card H ≤ p ^ k),
    (∀ H : Subgroup G, IsMulCommutative H → Nat.card H ≤ p ^ (2 * k)) := by
…
```