Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-04T20:18:53.298Z Has data issue: false hasContentIssue false
  • English
  • Français

Alternating trilinear forms and groups of exponent 6

Published online by Cambridge University Press:  09 April 2009

M. D. Atkinson
M. D. Atkinson
Affiliation:
The Queen's College, Oxford, England
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.

The theory of alternating bilinear forms on finite dimensional vector spaces V is well understood; two forms on V are equivalent if and only if they have equal ranks. The situation for alternating trilinear forms is much harder. This is partly because the number of forms of a given dimension is not independent of the underlying field and so there is no useful canonical description of an alternating trilinear form.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 1 , August 1973 , pp. 111 - 128
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Atkinson, M. D., D. Phil. thesis, (Oxford, 1970).Google Scholar
[2]Hall, M., ‘Solution of the Burnside problem for exponent 6’, Illinois. J. Math. 2 (1958), 764–786.CrossRefGoogle Scholar
[3]Higman, G. and Hall, P., ‘The p-length of a p-soluble group and reduction theorems for Burnside's problem’, Proc. London Math. Soc. (3) 7 (1956), 1–42.Google Scholar
[4]Higman, G., ‘The orders of relatively free groups’. Proc. Internat. Conf. Theory of Groups, Aust. Nat. Univ. Canberra 08 1965, 153–165, (Gordon and Breach, New York, 1967).Google Scholar
[5]Neumann, Hanna: Varieties of groups, (Berlin - Heidelberg - New York), Springer - Verlag (1967).CrossRefGoogle Scholar