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The study of abstract groups: presentations by generators and relations, free, finite, profinite and pro-p groups, subgroup structure, growth, and structural theorems. Claims stating or applying results about groups belong here; claims about group schemes, algebraic groups, or algebraic-geometry objects do not.

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 →Golod–Shafarevich theoremimportance · 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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