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More on finite groups with few defining relations

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

J. L. Mennicke  and
B. H. Neumann
J. L. Mennicke
Affiliation:
Fakultät für MathematikUniversität BielefeldD-4800 Bielefeld 1, Germany
B. H. Neumann
Affiliation:
Department of MathematicsInstitute of Advanced Studies Australian National University Canberra, ACT 2601 and Division of Mathematics and Statistics, Commonwealth Scientific and Industrial Research Organization, Canberra, ACT 2601, Australia
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Abstract

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Certain central products of the binary polyhedral groups with finite cyclic groups are here shown to have presentations with two generators and two defining relations; this disproves a conjecture of the second author, stated in J. Austral. Math. Soc. Ser. A 38 (1985), 230–240.

MSC classification

Secondary: 20F05: Generators, relations, and presentations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 1 , February 1989 , pp. 132 - 136
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Mennicke, J., ‘Über Heegarddiagramme vom Geschlecht zwei mit endlicher Fundamentalgruppe’, Arch. Math. 8 (1957), 192–198.CrossRefGoogle Scholar
[2]Mennicke, J., ‘Über endliche Fundamentalgruppen’, Unpublished manuscript (1956).Google Scholar
[3]Neumann, B. H., ‘Some finite groups with few defining relations’, J. Austral. Math. Soc. Ser. A 38 (1985), 230–240.CrossRefGoogle Scholar
[4]Threlfall, W. and Seifert, H., ‘Topologische Untersuchung der Diskontinuitätsbereiche endlicher Bewegungsgruppen des dreidimensionalen sphärischen Raumes’, Math. Ann. 104 (1931), 1–70.CrossRefGoogle Scholar
[5]Threlfall, W. and Seifert, H., ‘Topologische Untersuchung der Diskontinuitätsbereiche endlicher Bewegungsgruppen des dreidimensionalen sphärischen Raumes (Schluβ)’, Math. Ann. 107 (1933), 543–586.CrossRefGoogle Scholar