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Gilbert Baumslag

Faculty and Staff Profiles

Gilbert Baumslag

Distinguished Professor Emeritus


Additional Departments/Affiliated Programs::

Shepard Hall SH 279
Phone Number: 
(212) 650-5153
(212) 650-5381

Professor Baumslag has given keynote addresses in most conferences in infinite group theory world-wide. He has worked with many mathematicians and has had more than 30 doctoral students. He plays tennis and squash when he has time. Professor Baumslag is also the Director of the Center for Algorithms & Interactive Scientific Software (CAISSWebsite


Professor Baumslag received his B.Sc. Honours (Masters) and D.Sc. from the University of Witwatersrand.

He earned his Ph.D. from the University of Manchester in 1958; his thesis, written under the direction of Bernhard Neumann, was titled: Some aspects of groups with unique roots.

Courses Taught
  • Topics in Group Theory
  • Theoretical Computer Science
Research Interests

Professor Baumslag is currently working on research into combinatorial group theory, interface design, zero learning curve software including a package for statistics, new games based on group theory and the involvement of high school students and undergraduates in research. Over 150 papers, 2 books, 2 monographs.


1. Gilbert Baumslag and C. F. Miller, Reflections on some groups of B.H. Neumann, J. Group Theory, 1-11 (2009).

2. Gilbert Baumslag, C.F. Miller III and Douglas Troeger: Virtual properties of cyclically pinched one-relator groups. International J. Algebra and Computation, 19 (2) 213-227 (2009).

3. Gilbert Baumslag, Oleg Bogopolski, Benjamin Fine, Anthony Gaglione, Gerhard Rosenberger, Dennis Spellman: On some finiteness properties in infinite groups. Algebra Colloq., 15(1): 1-22 (2008)

4. Gilbert Baumslag: Groups with the same lower central sequences, L'Enseignement Mathematique (2) 54 (2008).

5. Gilbert Baumslag and C. F. Miller: The isomorphism problem for residually torsion-free nilpotent groups. pp. 1–20, Groups, Geometry and Dynamics. volume 1 (2007).

6. Gilbert Baumslag and C.F Miller, Finitely presented extensions by free groups, J. Group Theory 10(5): (2007), 723-729.

7. Gilbert Baumslag: Recognizing powers in nilpotent groups and nilpotent images of free groups. J. Aust. Math. Soc., 83(2): 149-155 (2007)

8. Gilbert Baumslag, Charles Miller III, Douglas Troeger: Reflections on the residual finiteness of one-relator groups. Groups Geom. Dyn., 1(3): 209-219 (2007)

9. Gilbert Baumslag, B. Fine, A. Gaglione, D. Spellman: Reflections on discriminating groups. J. Group Theory, 10(1): 87-98 (2007).

10. Gilbert Baumslag, Sean Cleary: Parafree one-relator groups. J. Group Theory, 9(2): 191-201 (2006).

11. Gilbert Baumslag, Subspaces, free subgroups and a theorem of Stallings, International Journal Pure and Comput., 17 (2006) 205–217.

12. Gilbert Baumslag, Benjamin Fine, Xiaowei Xu: Cryptosystems using linear groups. Appl. Algebra Engrg. Comm. Comput., 17(3-4): 205-217 (2006)

13. Gilbert Baumslag, B. Fine and X. Xu, A Public Key Cryptosystem Using the Modular Group, Baumslag, Fine and Xu. In Combinatorial group theory, discrete groups, and number theory, Contemp. Math., volume 421, pages 35-43. Providence, RI: Amer. Math. Soc., 2006.

14. Gilbert Baumslag, Benjamin Fine, A.M. Gaglione, D. Spellman: A note on nondiscrimination of nilpotent groups and Malcev completions. Combinatorial Group Theory, Discrete Groups, and Number Theory, Contemp. Math., 421, Amer. Math. Soc., Providence, RI, 2006: 29-34.

15. Gilbert Baumslag, T. Camps, B. Fine, G. Rosenberger, X. Xu: Designing key transport protocols using combinatorial group theory. Algebraic methods in cryptography, Contemp. Math., 418, Amer. Math. Soc., Providence, RI, 2006: 35-43

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