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Finite P-groups with unique maximal classes

Published online by Cambridge University Press:  20 January 2009

I. D. Macdonald
I. D. Macdonald
Affiliation:
University of Stirling
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Is it possible for a finite p-group to have only one conjugacy class of maximal size? This question was opened to public consideration in a paper [2] of John Meldrum dealing with the breadth of the wreath product of finite p-groups. His Theorem 21 gives a formula for the breadth of A wr B in terms of various constants including the breadths of A and B, a formula which differs according to whether or not A has a unique largest class. Hence the question.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 26 , Issue 2 , June 1983 , pp. 233 - 239
Copyright
Copyright © Edinburgh Mathematical Society 1983

References

REFERENCES

1.Knoche, H.-G., Über den Frobeniusschen Klassenbegriff in Nilpotenten Gruppen. II, Math. Z. 59 (1953), 8–16.Google Scholar
2.Meldrum, J. D. P., Centralisers in wreath products, Proc. Edinburgh Math. Soc. 22 (1979), 161–168.CrossRefGoogle Scholar