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Characteristics of GWrSn

Published online by Cambridge University Press:  24 October 2008

A. G. Williams
A. G. Williams
Affiliation:
University of Warwick
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Extract

The ‘characteristics’ of the wreath product GWrSn, where G is a finite group, are certain polynomials (to be defined in section 2) which are generating functions for the simple characters of GWrSn. Schur (8) first used characteristics of the symmetric group. Specht (9) defined characteristics for GWrSn and found a relation between the characteristics of GWrSn and those of Sn which determined the simple characters of GWrSn. The object of this paper is to describe the p-block structure of GWrSn in the case where p is not a factor of the order of G. We use the relationship between the characteristics of GWrSn and those of Sn, which we deduce from a knowledge of the simple characters of GWrSn (these can be determined, independently of Specht's work, by using Clifford theory).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 79 , Issue 3 , May 1976 , pp. 433 - 441
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

REFERENCES

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