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KindShowingImportancePrizesTopicGolod–Shafarevich theorem1 result

The Golod–Shafarevich theorem (1964): a finite pro-p group on d generators requires more than d²/4 defining relations; equivalently, a finitely presented pro-p group with at most d²/4 relations is infinite. Claims about the inequality, its refinements (e.g. Ershov–Jaikin), Golod–Shafarevich groups, and applications such as infinite class field towers belong here.

A finitely presented pro-p group with d generators and at most d^2/4 defining relations is infinite.
UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Group theoryimportance · settledImportance 0.12, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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