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Free Groups

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

Abstract

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.

References

  1. 4.
    Garrett Birkhoff, Lattice Theory, third edition, AMS Colloq. Publications, v. XXV, 1967. MR 37 #2638.Google Scholar
  2. 46.
    George M. Bergman, The diamond lemma for ring theory, Advances in Math. 29 (1978) 178–218. MR 81b :16001.Google Scholar
  3. 76.
    S. Peter Farbman, Non-free two-generator subgroups ofSL2 (ℚ), Publicacions Matemàtiques (Univ. Autònoma, Barcelona) 39 (1995) 379–391. MR 96k :20090.Google Scholar
  4. 85.
    Philip Hall, Some word-problems, J. London Math. Soc. 33 (1958) 482–496. MR 21 #1331.Google Scholar
  5. 142.
    B. L. van der Waerden, Free products of groups, Amer. J. Math. 70 (1948) 527–528. MR 10, 9d.Google Scholar

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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