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Orbit sizes, local subgroups and chains of p-groups

Part of: Structure and classification of infinite or finite groups Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

I. M. Isaacs
I. M. Isaacs
Affiliation:
Mathematics Department, University of Wisconsin480 Lincoln Drive, Madison WI 53706 USA e-mail: isaacs@math.wisc.edu
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Abstract

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Let G be a finite group that acts on a finite group V, and let p be a prime that does not divide the order of V. Then the p-parts of the orbit sizes are the same in the actions of G on the sets of conjugacy classes and irreducible characters of V. This result is derived as a consequence of some general theory relating orbits and chains of p-subgroups of a group.

MSC classification

Secondary: 20E45: Conjugacy classes 20C15: Ordinary representations and characters
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 3 , December 2001 , pp. 325 - 338
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Broué, M., ‘Scott modules and p-permutatiób modules: an approach through the Brauer morphism’, Proc. Amer. Math. Soc. 93 (1985), 401–408.CrossRefGoogle Scholar
[2]Isaacs, I. M., Character theory offinite groups (Dover, New York, 1994).Google Scholar
[3]Isaacs, I. M., ‘Alperin's conjecture and the subgroup structure of a finite group’, Rocky Mountain J. Math. 30 (2000), 237–255.CrossRefGoogle Scholar
[4]Knörr, R. and Robinson, G. R., ‘Some remarks on a conjecture of Alperin’, J. London Math. Soc. (2) 39 (1989), 48–60.Google Scholar