Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-27T15:37:07.810Z Has data issue: false hasContentIssue false
  • English
  • Français

Permutation characters

Published online by Cambridge University Press:  09 April 2009

Fiona M. Ross
Fiona M. Ross
Affiliation:
University of SydneySydney, N.S.W.
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.

We suppose throughout that G is a finite group with a faithful matrix representation X over the complex field. We suppose that X affords a character π of degree r whose values are rational (hence rational integers). If the matrices in some representation of G affording a character π0 are all permutation matrices, then π0 is called a permutation character. Permutation characters have non-negative integral values. In the general case, we consider what properties of permutation characters are true of π, and in particular, under what circumstances π is a permutation character. Note that assuming X to b faithful is equivalent to considering the image group X(G) instead of G.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 1 , February 1972 , pp. 76 - 90
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Brauer, R., ‘A note on theorems of Burnside and Blichfeldt’, Proc. Amer. Math. Soc. 15 (1964), 31–34.CrossRefGoogle Scholar
[2]Burnside, W., Theory of groups of finite order (New York: Dover 1955, 2nd edition 1911).Google Scholar
[3]Feit, W. and Thompson, J. G., ‘Solvability of groups of odd order’, Pacific J. Math. 13 (1963), 775–1029.CrossRefGoogle Scholar
[4]Hall, M., The theory of groups (New York: Macmillan, 1959).Google Scholar
[5]Littlewood, D. E., The theory of group characters (Oxford: University Press, 2nd edition 1950).Google Scholar
[6]Scott, W. R., Group theory (Englewood Cliffs, N.J.: Prentice-Hall, 1964).Google Scholar
[7]van der Waerden, B. L., Modern algebra vol. 1 (New York: Ungar, 1950).Google Scholar
[8]Wong, W. J., ‘Linear groups analogous to permutation groups’, Journ. Australian Math. Soc. 3 (1963), 180–184.CrossRefGoogle Scholar
[9]Wong, W. J., ‘On linear p-groups’, Journ. Australian Math. Soc. 4 (1964), 174–178.CrossRefGoogle Scholar