Free Groups

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


As motivation for the general investigation of universal constructions, the concept of a free group on a set X is defined, and such groups are constructed in three ways: As sets of group-theoretic terms in X modulo consequences of the group identities, as subgroups of sufficiently large direct product groups, and as groups of reduced words.


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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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