example of fibre product

Let G, G, and H be groups, and suppose we have homomorphismsMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath f:GH and f:GH. Then we can construct the fibre product G×HG. It is the following group:

{(g,g)G×G such that f(g)=f(g)}.

Observe that since f and f are homomorphisms, it is closed underPlanetmathPlanetmath the group operationsMathworldPlanetmath.

Note also that the fibre product depends on the maps f and F, although the notation does not reflect this.

Title example of fibre product
Canonical name ExampleOfFibreProduct
Date of creation 2013-03-22 14:08:38
Last modified on 2013-03-22 14:08:38
Owner archibal (4430)
Last modified by archibal (4430)
Numerical id 4
Author archibal (4430)
Entry type Example
Classification msc 14A15
Related topic Group
Related topic Homomorphism
Related topic CartesianProduct