Hostname: page-component-784d4fb959-wvrvt Total loading time: 0 Render date: 2025-07-14T11:58:45.417Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Information

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[2]Mennicke, J., ‘Über endliche Fundamentalgruppen’, Unpublished manuscript (1956).Google Scholar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