Alphabeta MathHow statement and proof provenance work
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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These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Poly-torsion-free abelian groups
Definition
A group G is poly-torsion-free abelian (PTFA) if it admits a finite subnormal series 1=G_0 ◁ G_1 ◁ ⋯ ◁ G_m=G in which every quotient G_{j+1}/G_j is torsion-free abelian. The trivial group is PTFA, using the length-zero series. The term “subnormal” means each G_j is normal in G_{j+1}; normality in all of G is not required.
Definition references
Depends on
Used by
- Localized Blanchfield pairings and higher-order rho-invariants Definition
- Integral and field PTFA group rings have compatible Ore fractions and involutions Lemma
- PTFA groups satisfy the finite Folner condition without a choice hypothesis Lemma
- PTFA subgroup extension preserves nonzero Blanchfield self-pairings Lemma
- PTFA augmentation detects projective injectivity without choice Theorem
- PTFA group rings embed in skew fields of fractions Theorem
Dependency tree · two levels
4 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
- Tim D. Cochran, Kent E. Orr, and Peter Teichner, “Knot concordance, Whitney towers and L²-signatures” (standard reference, not scraped)