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Permutation characters

Published online by Cambridge University Press:  09 April 2009

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

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