Alphabeta Math
False statementConstruction: AI-adaptedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-04
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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.

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  • 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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Because every coordinate group is finite, Zp is an additive torsion group

Statement

Because every coordinate group Z/pnZ is finite, the additive group of Zp is torsion.

Facts & Assumptions

Given: The additive group of Zp.

[L1]

The additive group of Zp is torsion-free (The additive group of Zp is torsion-free).

Refutation

technique · direct
1.1given

The element 1∈Zp is nonzero.

2.1L1step 1.1

If the additive group of Zp were torsion, some positive multiple of 1 would be 0. That contradicts [L1], since [L1] says that no nonzero element of Zp has finite order.

3.1step 1.1step 2.1∎

Therefore the statement is false. Finite coordinate groups do not force torsion in the inverse limit.

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