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Experimental Mathematics Volume 12, 2003 - Issue 4
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Original Articles

Irreducible Cyclic Presentations of the Trivial Group

George Havas ARC Centre for Complex Systems, School of Information Technology and Electrical Engineering, The University of Queensland, Queensland, 4072, Australia E-mail: [email protected]
&
Edmund F. Robertson School of Mathematics and Statistics, University of St. Andrews, North Haugh, St. Andrews, Fife KY16 9SS, Scotland E-mail: [email protected]
Pages 487-490 | Published online: 05 Apr 2012

REFERENCES

  • Burns , R. G. and Macedonńska , O. 1993 . “Balanced Presentations of the Trivial Group.” . Bull. London Math. Soc. , 25 : 513 – 526 . [Burns and Macedońska 93]
  • Dunwoody , M. J. “Cyclic Presentations and 3-Manifolds.” . Groups—Korea 1994 Proceedings . Edited by: Kim , A. C. and Johnson , D. L. pp. 47 – 55 . Berlin : de Gruyter. . [Dunwoody 95]
  • Edjvet , M. , Hammond , P. and Thomas , N. 2001 . “Cyclic Presentations of the Trivial Group.” . Experimental Mathematics , 10 : 303 – 306 . [Edjvet et al. 01]
  • The GAP Group . 2003 . GAP – Groups, Algorithms, and Programming, , Version 4.3. [GAP4 03], Available from World Wide Web http://www.gap-system.org
  • Havas , G. and Ramsay , C. 2000 . “Proving a Group Trivial Made Easy: A Case Study in Coset Enumeration.” . Bulletin of the Australian Mathematical Society , 62 : 105 – 118 . [Havas and Ramsay 00]
  • Havas , G. and Ramsay , C. 2003 . “Andrews-Curtis and Todd-Coxeter Proof Words.” . In Groups St Andrews 2001 in Oxford 232 – 237 . Cambridge , , UK : Cambridge University Press. . [Havas and Ramsay 03a], London Mathematical Society Lecture Note Series, 304
  • Havas , G. and Ramsay , C. 2003 . “Breadth-First Search and the Andrews-Curtis Conjecture.” . International Journal of Algebra and Computation , 13 : 61 – 68 . [Havas and Ramsay 03b]
  • Havas , G. , Ramsay , C. , Gamble , G. and Hulpke , A. 2003 . “ACE: A GAP 4 Package Providing an Interface to the Advanced Coset Enumerator.” [Havas et al. 03], Available from World Wide Web http://www.gap-system.org/Share/ace.html
  • Johnson , D. L. 1976 . Presentations of Groups Cambridge , , UK : Cambridge University Press. . [Johnson 76], London Mathematical Society Lecture Notes Series, 22
  • Johnson , D. L. 1980 . Topics in the Theory of Group Presentations Cambridge , , UK : Cambridge University Press. . [Johnson 80], London Mathematical Society Lecture Note Series, 42
  • Miasnikov , A. D. 1999 . “Genetic Algorithms and the Andrews-Curtis Conjecture.” . The International Journal of Algebra and Computation , 9 : 671 – 686 . [Miasnikov 99]
  • Neumann , B. H. 1979 . “Proofs.” . The Mathematical Intelligencer , 2 : 18 – 19 . [Neumann 79]

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