Gilbert Baumslag | Academic Influence

Gilbert Baumslag's AcademicInfluence.com Rankings

Gilbert Baumslag

Mathematics

#886

World Rank

#1560

Historical Rank

#385

USA Rank

Group Theory

#5

World Rank

#7

Historical Rank

#2

USA Rank

Measure Theory

#1240

World Rank

#1571

Historical Rank

#451

USA Rank

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Mathematics

Gilbert Baumslag's Degrees

PhD Mathematics University of Chicago
Bachelors Mathematics University of Chicago

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Why Is Gilbert Baumslag Influential?

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According to Wikipedia, Gilbert Baumslag was a Distinguished Professor at the City College of New York, with joint appointments in mathematics, computer science, and electrical engineering. He was director of the Center for Algorithms and Interactive Scientific Software, which grew out of the MAGNUS computational group theory project he also headed. Baumslag was also the organizer of the New York Group Theory Seminar.

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Gilbert Baumslag's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Some two-generator one-relator non-Hopfian groups (1962) (376)
Algebraic Geometry over Groups I. Algebraic Sets and Ideal Theory (1999) (303)
Algebraic Geometry over Groups (2000) (179)
On generalised free products (1962) (167)
On the residual finiteness of generalised free products of nilpotent groups (1963) (165)
Some aspects of groups with unique roots (1960) (137)
Automatic groups and amalgams (1991) (134)
Topics in combinatorial group theory (1993) (126)
Wreath products and p–groups (1959) (105)
The topology of discrete groups (1980) (103)
Subgroups of Direct Products of Free Groups (1984) (99)
A non-cyclic one-relator group all of whose finite quotients are cyclic (1969) (86)
Geometric and Computational Perspectives on Infinite Groups (1995) (84)
Automorphism Groups of Residually Finite Groups (1963) (84)
Groups with the same lower central sequence as a relatively free group (1967) (81)
Wreath products and finitely presented groups (1961) (78)
Generalized triangle groups (1987) (76)
Isoperimetric inequalities and the homology of groups (1993) (74)
Subgroups of finitely presented metabelian groups (1973) (72)
Open problems in combinatorial group theory (2005) (69)
Lecture notes on nilpotent groups (2007) (69)
Residual nilpotence and relations in free groups (1964) (67)
GROUPS WITH THE SAME LOWER CENTRAL SEQUENCE AS A RELATIVELY FREE GROUP. II. PROPERTIES (1969) (65)
The centre of groups with one defining relator (1967) (63)
Fibre products, non-positive curvature, and decision problems (2000) (55)
The algorithmic theory of polycyclic-by-finite groups☆ (1991) (54)
Wreath products and extensions (1963) (54)
Residually finite one-relator groups (1967) (52)
Algorithms and Classification in Combinatorial Group Theory (2011) (51)
On the residual nilpotence of certain one-relator groups† (1968) (49)
Two Theorems about Equationally Noetherian Groups (1997) (48)
Discriminating Completions of Hyperbolic Groups (2002) (45)
A finitely presented metabelian group with a free abelian derived group of infinite rank (1972) (45)
Some Unsolvable Problems about Elements and Subgroups of Groups. (1959) (43)
Unsolvable Problems About Small Cancellation and Word Hyperbolic Groups (1994) (42)
Constructable solvable groups (1976) (41)
Some Problems in One - Relator Groups (1973) (40)
Finitely Presented Metabelian Groups (1972) (39)
Positive one-relator groups (1971) (38)
Computable algebra and group embeddings (1981) (37)
On the integral homology of finitely-presented groups (1981) (36)
On varieties generated by a finitely generated group (1964) (33)
Finitely Presented Subgroups of Automatic Groups and their Isoperimetric Functions (1996) (31)
Algorithmically insoluble problems about finitely presented solvable groups, lie, and associative algebras (1985) (30)
The algorithmic theory of finitely generated metabelian groups (1994) (28)
Amalgamated products and finitely presented groups (1990) (27)
On the inverse limit of free nilpotent groups (1977) (27)
Malnormality is Decidable in Free Groups (1999) (25)
Some groups that are just about free (1967) (24)
Discriminating and co-discriminating groups (2000) (23)
Groups whose three-generator subgroups are free (1989) (23)
Automorphism groups of finitely generated nilpotent groups (1967) (23)
A finitely generated, infinitely related group with trivial multiplicator (1971) (23)
Cryptosystems using Linear Groups (2006) (22)
Residually finite groups with the same finite images (2019) (21)
Finitely generated cyclic extensions of free groups are residually finite (1971) (21)
Infinitely generated subgroups of finitely presented groups. Part II (1977) (20)
Some finitely generated, infinitely related metabelian groups with trivial multiplicator (1976) (20)
On the multiplicator of F/γcR (1980) (20)
On free D- groups† (1965) (18)
Some recognizable properties of solvable groups (1981) (18)
A non-Hopfian group (1962) (17)
A Course in Mathematical Cryptography (2015) (17)
Algorithmically insoluble problems about finitely presented solvable groups, lie and associative algebras. I (1986) (17)
Reflections on the residual finiteness of one-relator groups (2007) (17)
Some theorems on the free groups of certain product varieties (1967) (16)
Free subgroups of certain one-relator groups defined by positive words (1983) (16)
Some subgroup theorems for free -groups (1963) (16)
Experimenting with Infinite Groups, I (2004) (16)
A survey of groups with a single defining relation (1987) (16)
On a Problem of Lyndon (1960) (15)
Parallel poly-pushdown groups (1997) (15)
Review: Roger C. Lyndon and Paul E. Schupp, Combinatorial group theory (1979) (15)
On the residual nilpotence of some varietal products (1963) (14)
Subalgebras of finitely presented solvable Lie algebras (1977) (14)
Some reflections on cohomological dimension and freeness (1967) (14)
On Ascending Chain Conditions (1971) (14)
Direct decompositions of finitely generated torsion-free nilpotent groups (1975) (14)
A Remark on Generalised Free Products (1962) (13)
A remark on generalized free products (1962) (13)
Some Odd Finitely Presented Groups (1988) (13)
Parafree one-relator groups (2006) (13)
AUTOMORPHISM GROUPS OF NILPOTENT GROUPS. (1969) (12)
Automorphism Groups of Two Generator Metabelian Groups (1987) (12)
Roots and Wreath Products (1960) (12)
Algorithmically insoluble problems about finitely presented solvable groups, lie and associative algebras, II (1985) (11)
Groups with one defining relator (1964) (11)
Virtual Properties of cyclically pinched One-Relator Groups (2009) (11)
THE INTEGRAL HOMOLOGY OF FINITELY GENERATED METABELIAN GROUPS II (1982) (11)
A new look at finitely generated metabelian groups (2012) (11)
SOME REMARKS ON NILPOTENT GROUPS WITH ROOTS (1961) (11)
Groups with Cyclic Upper Central Factors (1960) (10)
Some reflections on proving groups residually torsion-free nilpotent. I (2010) (10)
Generalized Learning Problems and Applications to Non-commutative Cryptography (2011) (10)
Free Abelian $X$-groups (1986) (10)
Finite presentation of fibre products of metabelian groups (2003) (9)
Automatic Groups and Amalgams — A Survey (1992) (9)
A non-cyclic, locally free, free-by-cyclic group all of whose finite factor groups are cyclic (1972) (9)
Finitely generated residually torsion-free nilpotent groups. I (1999) (9)
Musings on Magnus (1993) (8)
Infinitely generated subgroups of finitely presented groups. I (1977) (8)
On abelian hopfian groups. I (1962) (8)
Affine Algebraic Sets and Some Infinite Finitely Presented Groups (1987) (8)
On the absence of cohomological finiteness in wreath products (1998) (7)
Direct summands of unrestricted direct sums of Abelian groups (1959) (6)
Some remarks on finitely presented algebras (1976) (6)
Free Exterior Powers of Nonfree Modules and Homology (1987) (6)
Torsion-free groups and amalgamated products (1970) (5)
A representation of the wreath product of two torsion-free abelian groups in a power series ring (1966) (5)
Localization, metabelian groups, and the isomorphism problem (2013) (5)
On the subalgebras of certain finitely presented algebras (1976) (5)
Equations in free metabelian groups. (1965) (5)
Experimenting and computing with infinite groups (1995) (5)
A generalisation of a theorem of Mal’cev (1961) (5)
Some remarks about multiplicators and finitely presented groups (1972) (5)
A finitely presented solvable group that is not residually finite (1973) (4)
The free metabelian group of rank two contains continuously many nonisomorphic subgroups (1988) (4)
Some open problems (1998) (4)
Residual properties of groups defined by basic commutators (2013) (4)
Finitely presented extensions by free groups (2007) (4)
On free metabelian products (1965) (4)
A non-free parafree group all of whose countable subgroups are free (1976) (4)
Groups acting on trees (1993) (4)
Challenge response password security using combinatorial group theory (2010) (4)
Reflections on some groups of B. H. Neumann (2009) (4)
The isomorphism problem for residually torsion-free nilpotent groups (2007) (4)
Virtually free-by-cyclic one–relator groups I (2008) (4)
Reflections on discriminating groups (2007) (3)
On Some Finiteness Properties in Infinite Groups (2008) (3)
Decomposability of finitely generated torsion-free nilpotent groups (2015) (3)
Products of abelian hopfian groups (1968) (3)
A subgroup theorem for some product varieties (1965) (3)
Reviews on infinite groups : as printed in Mathematical reviews 1940 through 1970, volumes 1-40 inclusive (1974) (3)
On generalised free products of torsion-free nilpotent groups I (1972) (2)
Finitely presented semigroups and associative aigebras (1978) (2)
Recognizing powers in nilpotent groups and nilpotent images of free groups (2007) (2)
One-Relator Groups: An Overview (2019) (2)
A remark on the multiplicative group of the division ring of a poly-infinite-cyclic group (1974) (2)
Finite factors in infinite ascending derived series (1957) (2)
A remark on finitely presented infinite-dimensional algebras (1990) (2)
Localization, completions and metabelian groups (2013) (2)
8. Elliptic Curve Cryptography (2015) (2)
A REMARK ON GROUPS WITH TRIVIAL MULTIPLICATOR. (1975) (2)
Groups with free 2-generator subsemigroups (1982) (1)
Subgroups of free metabelian groups (2010) (1)
A theorem on infinite groups (1957) (1)
Isoperimetric and isodiametric functions of group extensions (2020) (1)
Book Review: Word processing in groups (1994) (1)
On residual properties of generalized Hydra groups (2013) (1)
Experimenting with Infinite Groups, I: Tables (2004) (1)
Wilhelm Magnus, Collected Papers (1983) (1)
Encryption methods using formal power series rings (2006) (1)
4. Cryptographic Protocols (2015) (1)
Generalized free products and HNN extensions (1993) (1)
13. Commutative Gröbner Basis Methods (2015) (0)
OF THE AMERICAN MATHEMATICAL SOCIETY Volume 82 , Number 1 , January 1976 ON THE SUBALGEBRAS OF CERTAIN FINITELY PRESENTED ALGEBRAS BY (2007) (0)
Subspaces, Free Subgroups and a Theorem of Stallings (2006) (0)
On a problem of Plotkin concerning locally nilpotent groups (1964) (0)
A universal approach to groups and rings (1963) (0)
Residual properties and some applications (2007) (0)
Lie group techniques (2007) (0)
PSP volume 97 issue 3 Cover and Back matter (1985) (0)
Remembrances of Gilbert (2020) (0)
REFLECTIONS ON SOME GROUPS OF (0)
Basic notions and results (2007) (0)
A problem of Stallings on the direct square of a free group (1988) (0)
10. Non-Commutative Group Based Cryptography (2015) (0)
Free groups, the calculus of presentations and the method of Reidemeister and Schreier (1993) (0)
Lie and associative ring techniques and the commutator calculus (2007) (0)
7. Public Key Cryptography (2015) (0)
9. Basic Concepts from Group Theory (2015) (0)
5. Elementary Number Theoretic Techniques (2015) (0)
12. Further Applications Using Group Theory (2015) (0)
3. Cryptanalysis and Complexity (2015) (0)
2. Symmetric Key Cryptosystems (2015) (0)
Secure Passwords Using Combinatorial Group Theory (2018) (0)
6. Some Number Theoretic Algorithms (2015) (0)
15. Lattice-Based Cryptography (2015) (0)
Cryptographic systems using linear groups (2006) (0)
Geometric and computational perspectives on infinite groups : proceedings of a Joint DIMACS/Geometry Center Workshop, January 3-14 and March 17-20, 1994 (1996) (0)
A remark on hyperabelian groups (1961) (0)
SOME CRYPTOPRIMITIVES IN NONCOMMUTATIVE ALGEBRAIC CRYTOGRAPHY (2008) (0)
A remark on the subgroups of finitely generated groups with one defining relation (1986) (0)
The Weak Burnside Problem (1993) (0)
Affine algebraic sets and the representation theory of finitely generated groups (1993) (0)
11. Platform Groups and Braid Group Cryptography (2015) (0)
Bridson The homology of groups , profinite completions , and echoes of (2020) (0)
1. Basic Ideas of Cryptography (2015) (0)
14. Non-Commutative Gröbner Basis Methods (2015) (0)
Algorithmic problems for finitely generated nilpotent groups (2007) (0)
Recursively presentable groups, word problems and some applications of the Reidemeister-Schreier method (1993) (0)

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