Illinois Journal of Mathematics

On mathematical contributions of Paul E. Schupp

Ilya Kapovich

Article information

Source
Illinois J. Math., Volume 54, Number 1 (2010), 1-9.

Dates
First available in Project Euclid: 9 March 2011

https://projecteuclid.org/euclid.ijm/1299679735

Mathematical Reviews number (MathSciNet)
MR2776982

Zentralblatt MATH identifier
1210.01035

Citation

Kapovich, Ilya. On mathematical contributions of Paul E. Schupp. Illinois J. Math. 54 (2010), no. 1, 1--9. https://projecteuclid.org/euclid.ijm/1299679735

References

• A. V. Anisimov, The group languages, Kibernetika 4 (1971), 18–24.
• K. I. Appel and P. E. Schupp, The conjugacy problem for the group of any tame alternating knot is solvable, Proc. Amer. Math. Soc. 33 (1972), 329–333.
• K. I. Appel and P. E. Schupp, Artin groups and infinite Coxeter groups, Invent. Math. 72 (1983), 201–220.
• G. N. Arzhantseva and A. Yu. Ol'shanskii, Generality of the class of groups in which subgroups with a lesser number of generators are free, Mat. Zametki 59 (1996), 489–496.
• M. J. Dunwoody, The accessibility of finitely presented groups, Invent. Math. 81 (1985), 449–457.
• M. Greendlinger, Dehn's algorithm for the word problem, Comm. Pure Appl. Math. 13 (1960), 67–83.
• M. Greendlinger, On Dehn's algorithms for the conjugacy and word problems, with applications, Comm. Pure Appl. Math. 13 (1960), 641–677.
• M. Greendlinger, An analogue of a theorem of Magnus, Arch. Math. 12 (1961), 94–96.
• M. Gromov, Hyperbolic groups, Essays in group theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, 1987, pp. 75–263.
• M. Gromov, Random walk in random groups, Geom. Funct. Anal. 13 (2003), 73–146.
• J. Hamkins and A. G. Miasnikov, The halting problem is decidable on a set of asymptotic probability one, Notre Dame J. Formal Logic 47 (2006), 515–524.
• S. V. Ivanov and P. E. Schupp, On the hyperbolicity of small cancellation groups and one-relator groups, Trans. Amer. Math. Soc. 350 (1998), 1851–1894.
• V. Kaimanovich, I. Kapovich and P. Schupp, The Subadditive Ergodic Theorem and generic stretching factors of free group automorphisms, Israel J. Math. 157 (2007), 1–46.
• I. Kapovich, A. Miasnikov, P. Schupp and V. Shpilrain, Generic-case complexity, decision problems in group theory, and random walks, J. Algebra 264 (2003), 665–694.
• I. Kapovich, A. Miasnikov, P. Schupp and V. Shpilrain, Average-case complexity and decision problems in group theory, Adv. Math. 190 (2005), 343–359.
• I. Kapovich, I. Rivin, P. Schupp and V. Shpilrain, Densities in free groups and $\mathbb{Z}^k$, Visible Points and Test Elements, Math. Res. Lett. 14 (2007), 263–284.
• I. Kapovich and P. Schupp, Genericity, the Arzhantseva–Ol'shanskii method and the isomorphism problem for one-relator groups, Math. Ann. 331 (2005), 1–19.
• I. Kapovich and P. Schupp, Delzant's $T$-invariant, Kolmogorov complexity and one-relator groups, Comment. Math. Helv. 80 (2005), 911–933.
• I. Kapovich and P. Schupp, On group-theoretic models of randomness and genericity, Groups, Geometry and Dynamics 2 (2008), 383–404.
• I. Kapovich and P. Schupp, Random quotients of the modular group are rigid and essentially incompressible, J. Reine Angew. Math. 628 (2009), 91–119.
• I. Kapovich, P. Schupp and V. Shpilrain, Generic properties of Whitehead's Algorithm and isomorphism rigidity of random one-relator groups, Pacific J. Math. 223 (2006), 113–140.
• R. Lyndon and P. E. Schupp, Combinatorial group theory, Springer-Verlag, Berlin-New York, 1977. MR 0577064; reprinted in 'Classics in Mathematics' series, Springer-Verlag, Berlin, 2001. MR 1812024
• D. Muller and P. E. Schupp, Context-free languages, groups, the theory of ends, second-order logic, tiling problems, cellular automata, and vector addition systems, Bull. Amer. Math. Soc. (N.S.) 4 (1981), 331–334.
• D. Muller and P. E. Schupp, Groups, the theory of ends, and context-free languages, J. Comput. System Sci. 26 (1983), 295–310.
• D. Muller and P. E. Schupp, The theory of ends, pushdown automata, and second-order logic, Theoret. Comput. Sci. 37 (1985), 51–75.
• D. Muller and P. E. Schupp, Alternating automata on infinite trees, Theoret. Comput. Sci. 54 (1987), 267–276.
• D. Muller and P. E. Schupp, Simulating alternating tree automata by nondeterministic automata: New results and new proofs of the theorems of Rabin, McNaughton and Safra, Theoret. Comput. Sci. 141 (1995), 69–107.
• D. E. Muller, A. Saoudi and P. E. Schupp, Alternating automata, the weak monadic theory of the tree, and its complexity, Automata, languages and programming (Rennes, 1986), Lecture Notes in Comput. Sci., vol. 226, Springer, Berlin, 1986, pp. 275–283.
• D. E. Muller, A. Saoudi and P. E. Schupp, Alternating automata, the weak monadic theory of trees and its complexity, Theoret. Comput. Sci. 97 (1992), 233–244.
• A. G. Myasnikov and A. N. Rybalov, Generic complexity of undecidable problems, J. Symbolic Logic 73 (2008), 656–673.
• A. Yu. Ol'shanskii, Almost every group is hyperbolic, Internat. J. Algebra Comput. 2 (1992), 1–17.
• D. Osin, Peripheral fillings of relatively hyperbolic groups, Invent. Math. 167 (2007), 295–326.
• M. O. Rabin, Decidability of second-order theories and automata on infinite trees, Trans. Amer. Math. Soc. 141 (1969), 1–35.
• A. Rybalov, Generic complexity of Presburger arithmetic, Theory Comput. Syst. 46 (2010), 2–8.
• A. Saoudi, D. E. Muller and P. E. Schupp, Alternating automata, the weak monadic theory of trees and its complexity, Theoret. Comput. Sci. 97 (1992), 233–244.
• P. E. Schupp, On Dehn's algorithm and the conjugacy problem, Math. Ann. 178 (1968), 119–130.
• P. E. Schupp, On the conjugacy problem for certain quotient groups of free products, Math. Ann. 186 (1970), 123–129.
• P. E. Schupp, On Greendlinger's lemma, Comm. Pure Appl. Math. 23 (1970), 233–240.
• P. E. Schupp, Small cancellation theory over free products with amalgamation, Math. Ann. 193 (1971), 255–264.
• P. E. Schupp, A survey of small cancellation theory, Word problems: Decision problems and the Burnside problem in group theory (Conf. on Decision Problems in Group Theory, Univ. California, Irvine, Calif. 1969; dedicated to Hanna Neumann), Stud. Logic Found. Math., vol. 71, North-Holland, Amsterdam, 1973, pp. 569–589.
• P. E. Schupp, On the structure of Hamiltonian cycles in Cayley graphs of finite quotients of the modular group, Theoret. Comput. Sci. 204 (1998), 233–248.
• J. Stallings, Groups of cohomological dimension one, Applications of Categorical Algebra (Proc. Sympos. Pure Math., vol. XVIII, New York, 1968), Amer. Math. Soc., Providence, RI, 1970, pp. 124–128.