Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-24T17:13:13.718Z Has data issue: false hasContentIssue false
  • English
  • Français

Groups with trivial Schur multiplicator

Published online by Cambridge University Press:  09 April 2009

J. W. Wamsley
J. W. Wamsley
Affiliation:
The Flinders University of South Australia
Rights & Permissions [Opens in a new window]

Extract

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.

Let G be a finite group generated by n elements and defined by m relators, then G has a presentation where F free on generators x1, …, xn, and R is the normal closure in F of R1, …, Rm. The deficiency of this presentation is n – m and the deficiency of Gis the maximum over all presentations for G.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 4 , December 1973 , pp. 507 - 510
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]James, Rodney K., The Groups of Order p6 (p ≧ 3), Ph. D. Thesis University of Sydney, 1968.Google Scholar
[2]Macdonald, I. D., ‘On a class of finitely presented groups’, Canad. J. Math. 14 (1962), 602–613.CrossRefGoogle Scholar
[3]Neumann, B. H., ‘On some finite groups with trivial multiplicator’, Publ. Math. Debrecen 4 (1955), 190–194.CrossRefGoogle Scholar
[4]Swan, R. G., ‘Minimal resolutions for finite groups’, Topology 4 (1965), 193–208.CrossRefGoogle Scholar
[5]Wamsley, J. W., ‘Minimal presentations for certain group extensions’, Israel J. Math. 9 (1971), 459–463.CrossRefGoogle Scholar
[6]Wamsley, J. W., ‘The deficiency of metacyclic groups’, Proc. Amer. Math. Soc. 24 (1970), 724–726.Google Scholar