Alphabeta Math
False statementConstruction: AI-adaptedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck passjudge pass (gpt-5.6-terra)audited 2026-08-28
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The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

  • Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
  • AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
  • AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

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FALSE: the base group may collapse in an HNN extension

Statement

In an HNN extension, a nontrivial element of the base group can become trivial.

Facts & Assumptions

Given: An HNN extension of a base group A.

[L1]

The canonical map from the base group into its HNN extension is injective. (The base group embeds in its HNN extension)

Refutation

technique · direct
1.1

If a nontrivial element of A became trivial in the HNN extension, the canonical map A→G would identify it with eA.

L1given
2.1

That contradicts the injectivity stated in [L1]. Hence the statement is false.

L1step 1.1algebra∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

2 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources