A Cook’s Tour of Other Universal Constructions

  • George M. Bergman
Part of the Universitext book series (UTX)


Having carefully examined the free group construction, we now explore other universal constructions, noting similarities and differences. The examples studied include groups presented by generators and relations, Burnside groups, products and coproducts of groups (leading to the contrast between left and right universal constructions), similar constructions for monoids, rings, and Boolean rings, and constructions connecting one sort of structure to another (e.g., abelianizations of groups). For perspective, we also look at the topological constructions of Stone-Čech compactification, and of universal covering spaces.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • George M. Bergman
    • 1
  1. 1.Department of MathematicsUniversity of California, BerkeleyBerkeleyUSA

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