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.
- 4.Garrett Birkhoff, Lattice Theory, third edition, AMS Colloq. Publications, v. XXV, 1967. MR 37 #2638.Google Scholar
- 46.George M. Bergman, The diamond lemma for ring theory, Advances in Math. 29 (1978) 178–218. MR 81b :16001.Google Scholar
- 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
- 85.Philip Hall, Some word-problems, J. London Math. Soc. 33 (1958) 482–496. MR 21 #1331.Google Scholar
- 142.B. L. van der Waerden, Free products of groups, Amer. J. Math. 70 (1948) 527–528. MR 10, 9d.Google Scholar