Robert H. Gilman


Professor of Mathematics and
Director of the Algebraic Cryptology Center
Stevens Institute of Technology
Hoboken, NJ 07030

Phone (201) 216-5440, Fax (201) 216-8321

Publications

Random equations in nilpotent groups.
J. Algebra 352 (2012) 192--214, with Alexei G. Myasnikov and Vitali Roman'kov. arXiv .
Random equations in free groups.
Groups Complex. Cryptol. 3 (2011) 257--284, with Alexei G. Myasnikov and Vitalii Roman'kov . abstract .
Exponentially generic subsets of groups.
Illinois J. Math. 54 (2010) 371--388, with Alexei G. Miasnikov and Denis Osin. arXiv .
A geometric zero-one law.
J. Symbolic Logic 74 (2009) 929--938, with Yuri Gurevich and Alexei G. Miasnikov. pdf.
Solving one-variable equations in free groups.
J. Group Theory 12 (2009) no. 2, 317--330, with Dimitri Bormotov and Alexei G. Myasnikov . pdf.
New developments in commutator key exchange.
Proc. First Int. Conf. on Symbolic Computation and Cryptography (SCC-2008), Beijing, 2008, with Alexei G. Miasnikov, Alexei D. Myasnikov, and Alexander Ushakov. pdf.
A characterisation of virtually free groups.
Arch. Math. (Basel) 89 (2007) 289--295, with Susan Hermiller, Derek Holt, and Sarah Rees . pdf.
Report on generic case complexity.
Herald of Omsk University, Special Issue, 2007, 103-110, with A. G. Miasnikov, A. D. Myasnikov, and A. Ushakov. pdf.
Automatic quotients of free groups.
J. Pure Appl. Algebra 202 (2005) 313--324.pdf .
Formal languages and their application to combinatorial group theory. Groups, languages, algorithms.
1--36, Contemp. Math., 378, Amer. Math. Soc., Providence, RI, 2005. pdf.
One variable equations in free groups via context free languages.
Computational and experimental group theory, 83--88, Contemp. Math., 349, Amer. Math. Soc., Providence, RI, 2004, with Alexei G. Myasnikov. pdf.
Word hyperbolic semigroups.
Math. Proc. Cambridge Philos. Soc. 136 (2004) 513--524, with Andrew Duncan . pdf.
On the definition of word hyperbolic groups.
Math. Z. 242 (2002) 529--541.pdf.
Context-free languages of sub-exponential growth.
J. Comput. System Sci. 64 (2002) 308--310, with Martin Bridson. pdf.
Web version of three talks on groups and formal languages.
On groups whose word problem is solved by a nested stack automaton.
Unpublished, with Michael Shapiro. pdf.
Combing nilpotent and polycyclic groups.
Internat. J. Algebra Comput. 9 (1999) 135--155, with Derek Holt and Sarah Rees. pdf.
Formal language theory and the geometry of 3-manifolds.
Comment. Math. Helv. 71 (1996) 525--555, with Martin Bridson. pdf.
A shrinking lemma for indexed languages.
Theoret. Comput. Sci. 163 (1996) 277--281. pdf.
Formal languages and infinite groups.
Geometric and computational perspectives on infinite groups (Minneapolis, MN and New Brunswick, NJ, 1994) 27--51, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 25, Amer. Math. Soc., Providence, RI, 1996. pdf.
Automatic groups and string rewriting.
Term rewriting (Font Romeux, 1993) 127--134, Lecture Notes in Comput. Sci., 909, Springer, Berlin, 1995. pdf.
On bounded languages and the geometry of nilpotent groups.
Combinatorial and geometric group theory (Edinburgh, 1993) 1--15, London Math. Soc. Lecture Note Ser., 204, Cambridge Univ. Press, Cambridge, 1995, with Martin Bridson. pdf .
The geometry of cycles in the Cayley diagram of a group.
The mathematical legacy of Wilhelm Magnus: groups, geometry and special functions (Brooklyn, NY, 1992) 331--340, Contemp. Math., 169, Amer. Math. Soc., Providence, RI, 1994. pdf.
A remark about combings of groups.
Internat. J. Algebra Comput. 3 (1993) 575--581, with Martin Bridson. pdf .
Verifying that a group is virtually free.
Internat. J. Algebra Comput. 1 (1991) 339--351.
Periodic behavior of linear automata.
Dynamical systems (College Park, MD, 1986–87) 216--219, Lecture Notes in Math., 1342, Springer, Berlin, 1988.
Groups with a rational cross-section.
Combinatorial group theory and topology (Alta, Utah, 1984) 175--183, Ann. of Math. Stud., 111, Princeton Univ. Press, Princeton, NJ, 1987.
Classes of linear automata.
Ergodic Theory Dynam. Systems 7 (1987) 105--118.
An application of ultraproducts to finite groups.
Proceedings of the Rutgers group theory year, 1983--1984 (New Brunswick, N.J., 1983--1984) 409--412, Cambridge Univ. Press, Cambridge, 1985.
On the existence of cyclic surface kernels for pairs of Fuchsian groups.
J. London Math. Soc. (2) 30 (1984) no. 3, 451--464, witth Jane Gilman.
Computations with rational subsets of confluent groups.
EUROSAM 84 (Cambridge, 1984) 207--212, Lecture Notes in Comput. Sci., 174, Springer, Berlin, 1984.
Enumerating infinitely many cosets.
Computational group theory (Durham, 1982) 51--55, Academic Press, London, 1984.
Characteristically simple aleph-nought categorical groups.
J. Symbolic Logic 49 (1984) 900--907.
Finite groups with standard components of Lie type over fields of characteristic two.
J. Algebra 80 (1983) no. 2, 383--516, with Robert Griess.
Enumeration of double cosets.
J. Pure Appl. Algebra 26 (1982) 183--188.
Odd standard components.
The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979) pp. 85--90, Proc. Sympos. Pure Math., 37, Amer. Math. Soc., Providence, R.I., 1980.
Finite groups with small unbalancing 2-components.
Pacific J. Math. 83 (1979) no. 1, 55--106, with Ronald Solomon.
Presentations of groups and monoids.
J. Algebra 57 (1979) 544--554.
Finite quotients of the automorphism group of a free group.
Canad. J. Math. 29 (1977) 541--551.
Components of finite groups.
Comm. Algebra 4 (1976) 1133--1198.
Finite groups with Sylow 2-subgroups of class two. I, II.
Trans. Amer. Math. Soc. 207 (1975) 1--101; ibid. 207 (1975) 103--126, with Daniel Gorenstein.
A combinatorial identity with applications to representation theory.
Illinois J. Math. 17 (1973) 347--351.
Complements to solvable Hall subgroups.
Proc. Amer. Math. Soc. 27 (1971) 241--243.

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Revised 02/2014