False statementConstruction: Literature-sourcedVerification: AI-generatedPipeline-generatedprecheck passverified 2026-09-24 (gpt-6-sol)

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Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
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Multiplier defined as H²(G,C×)

Statement

For every group $G$ , the Schur multiplier is defined as $H^{2} (G; C^{\times})$ .

Facts & Assumptions

Given: Use the convention in Schur multiplier.

Refutation

technique · direct

1.1given

Schur multiplier defines $M (G) = H_{2} (G; Z)$ . The group $H^{2} (G; C^{\times})$ is a degree-two cohomology group with different coefficients and is not the specified definition. No comparison theorem is needed to refute a claim about which definition this library uses.

2.1step 1.1contradiction∎

It is therefore false to present $H^{2} (G; C^{\times})$ as this library's definition of the multiplier.

Depends on

Schur multiplier

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

Clara Löh, Group Cohomology (standard reference, not scraped)