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A computer-aided analysis of some finitely presented groups

Part of: Group theory and generalizations Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

M. F. Newman  and
E. A. O'Brien
M. F. Newman
Affiliation:
Mathematics Research Section School of Mathematical SciencesAustralian National UniversityGPO Box 4, ACT 2601, Australia
E. A. O'Brien
Affiliation:
Mathematics Research Section School of Mathematical SciencesAustralian National UniversityGPO Box 4, ACT 2601, Australia
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Abstract

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We answer some questions which arise from a recent paper of Campbell, Heggie, Robertson and Thomas on one-relator free products of two cyclic groups. In the process we show how publicly accessible computer programs can be used to help answer questions about finite group presentations.

MSC classification

Secondary: 20-04: Explicit machine computation and programs (not the theory of computation or programming) 20F05: Generators, relations, and presentations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 53 , Issue 3 , December 1992 , pp. 369 - 376
Copyright
Copyright © Australian Mathematical Society 1992

References

Campbell, Colin M., Heggie, Patricia M., Robertson, Edmund F. and Thomas, Richard M. (1992), ‘Finite one-relator products of two cyclic groups with the relator of arbitrary length’, J. Austral. Math. Soc. (Ser. A) 53, 351–367.Google Scholar
Cannon, John J., Dimino, Lucien A., Havas, George and Watson, Jane M. (1973), ‘Implementation and analysis of the Todd-Coxeter algorithm’, Math Comput. 27, 463–490.CrossRefGoogle Scholar
Cannon, John J. (1984), ‘An Introduction to the Group Theory Language, Cayley’ in: Computational Group Theory (Durham, 1982), (Academic Press, London) pp. 145–183.Google Scholar
Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A. and Wilson, R.A. (1985), Atlas of finite groups (Clarendon Press, Oxford).Google Scholar
Felsch, Volkmar (1989), SPAS User's Reference Manual (Lehrstuhl D für Mathematik, RWTH Aachen).Google Scholar
Havas, George (1974), ‘A Reidemeister-Schreier Program’ in: Proc. Second Internat. Conf. Theory of Groups (Canberra, 1973), Lecture Notes in Math. 372 (Springer-Verlag, Berlin) pp. 82–89.Google Scholar
Havas, George and Sterling, Leon S. (1979), ‘Integer matrices and abelian groups’ in: EUROSAM '79 (Marseille, 1979), Lecture Notes in Comput. Sci. 72 (Springer-Verlag, Berlin) pp. 431–451.Google Scholar
Havas, George and Newman, M.F. (1980), ‘Application of computers to questions like those of Burnside’ in: Burnside Groups (Bielefeld, 1977), Lecture Notes in Math. 806 (Springer-Verlag, Berlin) pp. 211–230.CrossRefGoogle Scholar
Havas, George, Kenne, P.E., Richardson, J.S. and Robertson, E.F. (1984), ‘A Tietze Transformation Program’ in: Computational Group Theory (Durham, 1982) (Academic Press, London) pp. 145–183.Google Scholar
Kenne, P.E. (1990), ‘Some new efficient soluble groups’, Comm. Algebra 18, 2747–2753.CrossRefGoogle Scholar
Neubüser, J. (1982), ‘An elementary introduction to coset table methods in computational group theory’ in: Groups - St Andrews 1981, London Math. Soc. Lecture Note Ser. 71 (Cambridge University Press, London) pp. 1–45.Google Scholar
Neubüser, Joachim and Sidki, Said (1988), ‘Some computational approaches to groups given by a finite presentation’, Mathematica Universitaria 7, 77–120, De Janeiro, Rio.Google Scholar
Slattery, Michael C. (1985), ‘Solution to AMS Notices Query No. 308’, CAYLEY Bulletin 2, 37–39, Sydney University.Google Scholar