Table of Contents
Algebra
Volume 2014 (2014), Article ID 379030, 12 pages
http://dx.doi.org/10.1155/2014/379030
Research Article

The Relatively Free Groups Satisfy Noncentral Commutative Transitivity

1Department of Mathematics, U.S. Naval Academy, Annapolis, MD 21402, USA
2Department of Mathematics, Temple University, Philadelphia, PA 19122, USA
3Department of Statistics, Temple University, Philadelphia, PA 19122, USA

Received 22 May 2014; Accepted 25 July 2014; Published 1 October 2014

Academic Editor: Antonio M. Cegarra

Copyright © 2014 Anthony M. Gaglione et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Neumann, Varieties of Groups, Springer, New York, NY, USA, 1967. View at MathSciNet
  2. N. Harrison, “Real length functions in groups,” Transactions of the American Mathematical Society, vol. 174, pp. 77–106, 1972. View at Publisher · View at Google Scholar · View at MathSciNet
  3. B. Baumslag, “Residually free groups,” Proceedings of the London Mathematical Society, vol. 17, no. 3, pp. 402–418, 1967. View at Google Scholar · View at MathSciNet
  4. P. M. Cohn, Universal Algebra, Harper & Row, New York, NY, USA, 1965. View at MathSciNet
  5. A. M. Gaglione, S. Lipschutz, and D. Spellman, “Discrimination and separation in the metabelian variety,” Contemporary Mathematics, vol. 583, pp. 129–142, 2012. View at Google Scholar
  6. F. Levin and G. Rosenberger, “On power-commutative and commutation-transitive groups,” in Proceedings of Groups—St Andrews 1985, vol. 121 of London Mathematical Society Lecture Note Series, pp. 249–253, 1985. View at Google Scholar
  7. V. N. Remeslennikov and R. Stöhr, “On the quasivariety generated by a non-cyclic free metabelian group,” Algebra Colloquium, vol. 11, no. 2, pp. 191–214, 2004. View at Google Scholar · View at MathSciNet · View at Scopus
  8. B. Fine, A. G. Myasnikov, A. M. Gaglione, and D. Spellman, “Discriminating groups,” Journal of Group Theory, vol. 4, no. 4, pp. 463–474, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. G. Grätzer, Universal Algebra, Van Nostrand, Princeton, NJ, USA, 1968. View at MathSciNet
  10. A. Myasnikov and V. Remeslennikov, “Algebraic geometry over groups II. Logical foundations,” Journal of Algebra, vol. 234, no. 1, pp. 225–276, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. O. Chapuis, “-free metabelian groups,” The Journal of Symbolic Logic, vol. 62, no. 1, pp. 159–174, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. G. Baumlslag, R. McKhailov, and K. E. Orr, A New Look at Finitely Generated Metabelian Groups, vol. 582 of Contemporary Mathematics, American Mathematical Society, Providence, RI, USA, 2012.
  13. R. C. Lyndon, “Two notes on nilpotent groups,” Proceedings of the American Mathematical Society, vol. 3, pp. 579–583, 1952. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. W. Magnus, A. Karrass, and D. Solitar, Combinatorial Group Theory, John Wiley & Sons, New York, NY, USA, 1966.
  15. G. Baumslag, Lecture Notes on Nilpotent Groups, AMS, Providence, RI, USA, 1971.
  16. A. M. Gaglione and D. Spellman, “The persistence of universal formulae in free algebras,” Bulletin of the Australian Mathematical Society, vol. 36, no. 1, pp. 11–17, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. S. Moran, “A subgroup theorem for free nilpotent groups,” Transactions of the American Mathematical Society, vol. 103, pp. 495–515, 1962. View at Publisher · View at Google Scholar · View at MathSciNet