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.

  • 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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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
1.1

The element 1∈Zp is nonzero.

given
2.1

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.

L1step 1.1
3.1

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

step 1.1step 2.1∎

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