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On the number of p-blocks of a p-soluble group

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

John Cossey
John Cossey
Affiliation:
Mathematics Department, Faculty of Science, Australian National University, GPO Box 4, Canberra 2601, Australia
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Abstract

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A technique is described for calculating the number of block ideals of FG, where F is a algebraically closed field of characteristic p, and where G is a p-soluble finite group. Among its consequences are the following: if U is a G-invariant irreducible FOp′(G)-module, then there is a unique block ideal of FG whose restriction to Op′(G) has all its composition factors isomorphic to U; and if G has p′-length 1, the number of block ideals of FG is the number of G-conjugacy classes of Op′(G)

MSC classification

Secondary: 20C05: Group rings of finite groups and their modules
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 41 , Issue 3 , December 1986 , pp. 339 - 342
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Cliff, Gerald H., ‘On modular representations of p-solvable groups’, J. Algebra 47 (1977), 129–137.CrossRefGoogle Scholar
[2]Gorenstein, D., Finite groups (Harper and Row, New York 1968).Google Scholar
[3]Huppert, B. and Blackburn, N., Finite groups II (Grundlehren der Math. 242, Springer Verlag, Berlin, Heidelberg, New York, 1982).CrossRefGoogle Scholar
[4]Isaacs, I. M., ‘Extensions of group representations over arbitrary fields’, J. Algebra 68 (1981), 54–74.CrossRefGoogle Scholar