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Free products with amalgamation along monomorphisms
Definition
If and are injective homomorphisms, their pushout is called the free product with amalgamation and is denoted . The quotient construction is A group pushout is the quotient of a free product by the amalgamating relations, and injectivity means the trivial-kernel condition of A group homomorphism is injective if and only if its kernel is trivial. The notation anticipates identifying with its two images, but injectivity of the canonical maps is a theorem, not part of this definition.
Depends on
Used by
- Amalgamation over the trivial group is the ordinary free product Corollary
- Transversal normal-form data for an amalgamated free product Definition
- Conventions and proved scope for free products and amalgamation Remark
- A free product with amalgamation has the factor presentations plus the amalgamating relations Theorem
Dependency tree · next 3 levels
Direct dependencies and their dependencies through the next three levels: 38 results over 13 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)