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Pushouts of group homomorphisms
Definition
Given homomorphisms and as in Monoid homomorphism and group homomorphism, a pushout is a group with homomorphisms and such that , and such that every compatible pair , factors through a unique with and . The maps need not be injective.
Depends on
Used by
- A pushout along an isomorphism is isomorphic to the other factor Corollary
- Free products with amalgamation along monomorphisms Definition
- A pushout along an isomorphism recovers the other group Example
- The kernels of the amalgamating maps are killed in the opposite canonical maps to a group pushout Proposition
- Conventions and proved scope for free products and amalgamation Remark
- A group pushout is the quotient of a free product by the amalgamating relations Theorem
- Normal form theorem for free products with amalgamation Theorem
Dependency tree · next 3 levels
Direct dependencies and their dependencies through the next three levels: 10 results over 10 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.
Sources
- George D. Torres, Combinatorial Group Theory, §2 (standard reference, not scraped)
- B. H. Neumann, Lectures on Topics in the Theory of Infinite Groups, Ch. 9 (standard reference, not scraped)