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Conjugacy in groups with dihedral 3-normalisers

Published online by Cambridge University Press:  18 May 2009

N. K. Dickson
N. K. Dickson
Affiliation:
University of Glasgow, Department of Mathematics, University Gardens, Glasgow, Scotland, G12 8QW
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Much work has been carried out on the classification of finite simple groups in terms of the structures of centralisers of involutions. However, it is sometimes the case that these classification results cannot be applied to particular problems even although information is available about one conjugacy class of involutions. The trouble is that information about the other classes can be almost non-existent. In this paper we deal with a situation where character theory can be employed to give a strong connection between the orders of centralisers of different classes of involutions, enabling information about one class to be used to give information about other classes. We prove the following result.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 18 , Issue 2 , July 1977 , pp. 167 - 173
Copyright
Copyright © Glasgow Mathematical Journal Trust 1977

References

REFERENCES

1.Dornhoff, L., Group Representation Theory (2 vols.) (Dekker, 1971).Google Scholar
2.Gorenstein, D., Finite Groups (Harper and Row, 1968).Google Scholar
3.Higman, G., Odd characterisations of finite simple groups, Lecture Notes (University of Michigan, 1968).Google Scholar