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A computer aided study of a group defined by fourth powers

Published online by Cambridge University Press:  17 April 2009

M.F. Newman
M.F. Newman
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
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Abstract

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There is a group defined by fourth powers which did not yield to attempts to determine its order by coset enumerations. This group has now been shown to be infinite with the aid of a computer. An outline of the method is given as well as a simple direct proof inspired by the results of further computer calculations.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 14 , Issue 2 , April 1976 , pp. 293 - 297
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Burnside, W., “On an unsettled problem in the theory of discontinuous groups”, Quart. J. Math. 33 (1902), 230–238.Google Scholar
[2]Coxeter, H.S.M. and Moser, W.O.J., Generators and relations for discrete groups (Ergebnisse der Mathematik und ihrer Grenzgebiete, 14. Springer-Verlag, Berlin, Göttingen, Heidelberg, 1957).CrossRefGoogle Scholar
[3]Havas, George, “A Reidemeister-Schreier program”, Proc. Second Internat. Conf. Theory of Groups, Canberra, 1973, 347–356 (Lecture Notes in Mathematics, 372. Springer-Verlag, Berlin, Heidelberg, New York, 1974).Google Scholar
[4]Leech, John, “Coset enumeration on digital computers”, Proc. Cambridge Philos. Soc. 59 (1963), 257–267.Google Scholar
[5]Macdonald, I.D., “A computer application to finite p-groups”, J. Austral. Math. Soc. 17 (1974), 102–112.Google Scholar
[6]Tobin, John Joseph, “On groups of exponent four” (PhD thesis, Manchester University, Manchester, 1954).Google Scholar
[7]Warnsley, J.W., “Computation in nilpotent groups (theory)”, Proc. Second Internat. Conf. Theory of Groups, Canberra, 1973, 691–700 (Lecture Notes in Mathematics, 372. Springer-Verlag, Berlin, Heidelberg, New York, 1974).Google Scholar