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Nonabelian extension obstruction in H^3
Remark
The classification theorem on this page assumes the Axiom of Choice and an abelian kernel with a specified action. For a possibly nonabelian kernel , assume Choice and prescribe an outer action .
Then Nonabelian extension obstruction and torsor under choice supplies an obstruction in that vanishes exactly when an extension exists. When one exists, the equivalence classes form a torsor under . In general the torsor has no preferred zero class; a chosen base extension identifies it with the group.
Depends on
Used by
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Dependency tree · two levels
9 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
- Samuel Eilenberg and Saunders Mac Lane, Cohomology Theory in Abstract Groups. II: Group Extensions with a non-Abelian Kernel, Annals of Mathematics (1947) (standard reference, not scraped)
- Clara Loh, Group Cohomology, SS 2019 (standard reference, not scraped)
- Caroline Lassueur, Cohomology of Groups, SS 2021 (standard reference, not scraped)