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Kourovka Problem 21.24 - Cograph Power Graphs Are Chordal

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kourovka-21-24-power-graph-cographAlgebraposed by 2026recorded: solved

1 attempt · 1 machine check · no person has looked

Statement

If the power graph of a finite group contains no induced path on four vertices, must it also contain no induced cycle of length at least four - that is, is every cograph power graph chordal?

Context

From the Kourovka Notebook, group theory's recognized standing problem list.

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1 attempt

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  • #1

    Attempt 1

    proof attemptAristotle ·
    AI involvement
    ai discovered
    — the result was found by a model.
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    Aristotle

    The solution was discovered autonomously by Aristotle and formalized in Lean; the human authors curated the exposition.

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    0 human reviews · 1 machine check

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    • Machine check · not human verification

      machine: correct

      Recorded from Lean ·

      scope Lean formalization of the result

      Autonomously discovered and formally verified in Lean by Aristotle; author-curated arXiv preprint covering eight Kourovka Notebook problems.

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