Gilbert Baumslag

Gilbert Baumslag (born April 20, 1933 in Johannesburg , † October 20, 2014 ) was an American mathematician from South Africa.

Baumslag studied at the University of Witwatersrand with a bachelor's degree in 1953 and a master's degree (Honors) in 1955 and received his doctorate in 1958 under Bernhard Neumann at Victoria University Manchester (Some Aspects of Groups with Unique Roots). He was then a lecturer at the University of Manchester in 1958/69 , an instructor at Princeton University in 1959/60 and from 1962 Assistant Professor at the Courant Institute at New York University, where he also became an Associate Professor. In 1964 he became a professor at the City University of New York , from 1969 to 1973 he was a professor at Rice University and then at City College of the City University of New York. From 1973 he was Distinguished Professor there.

He dealt with combinatorial group theory and infinite groups. With Donald Solitar he introduced tree lag solitar groups in 1962 , generated by the relation . Examples are , the free Abelian group with two generators, and , which is the fundamental group of the Klein bottle . is an example of an infinite group that is not of the Hopf type. Finding such an example (with a relation) was also the original motivation of Baumslag and Solitar ( Graham Higman had claimed in 1951 that all finally presented groups with a relation were of the Hopf type). ${\displaystyle B(m,n)}$ ${\displaystyle ba^{m}b^{-1}=a^{n}}$ ${\displaystyle B(1,1)}$ ${\displaystyle B(1,-1)}$ ${\displaystyle B(2,3)}$

Baumslag also initiated research on para-free groups , which are in many ways similar to free groups, but are not identical to them, as Baumslag showed.

He studied algorithmic group theory and was director of the Center for Algorithms & Interactive Scientific Software (CAISS) at the City College of New York. He also organized the New York Group Theory Seminar.

Most recently, he also dealt with math education including associated software, engaging high school students and undergraduates in research, and games based on group theory. He also worked on a public key encryption system based on the module group.

He was a student of Wilhelm Magnus and edited his Collected Papers with Bruce Chandler in 1984.

In 1976 he received a D.Sc. of the University of Witwatersrand. He was from 1965 Sloan Research Fellow at Rice University. In 1968/69 he was at the Institute for Advanced Study . In 2012 he became a Fellow of the American Mathematical Society .

He had been married since 1959 and had two children.

Fonts (selection)

• Groups with the same lower central sequence as a relatively free group, 2 parts, Transactions AMS, Volume 129, 1967, pp. 308-321, Volume 142, 1969, pp. 507-538
• with Donald Solitar: Some two-generator one-relator non-Hopfian groups, Bulletin of the American Mathematical Society, Volume 68, 1962, pp. 199-201, Project Euclid
• with Urs Stammbach: A non-free parafree group all of whose countable subgroups are free, Mathematische Zeitschrift, Volume 148, 1976, pp. 63–65
• Lecture notes on nilpotent groups, AMS 1971
• with Charles F. Miller: Algorithms and Classification in Combinatorial Group Theory, Springer 1992
• Topics in combinatorial group theory, Birkhäuser 1993
• with Benjamin Fine, Martin Kreuzer, Gerhard Rosenberger: A course in mathematical cryptography, De Gruyter 2015

Web links

• Obituary notice published in the New York Times, 2014
• Website at the CUNY

Individual evidence

1. ↑ Birth and career data according to American Men and Women of Science , Thomson Gale 2004
2. ↑ Gilbert Baumslag in the Mathematics Genealogy Project (English)
3. ↑ Baumslag-Solitar group , Encyclopedia of Mathematics, Springer
4. ↑ A finitely presented group G is of the Hopf type if it is not isomorphic to one of the factor groups G \ H with respect to a proper subgroup H of G. Further examples of infinite groups that are not of the Hopf type are the real numbers and the tester groups
5. ↑ Para Free groups, exploring the work of Gilbert Baumslag , Berstein Seminar, 2015
6. ^ 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., Vol. 421, 2006, pp. 35-43.